Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D8×#595 | C2 | semidirect |
| 2. #14545182 | C2 | direct (N × H) |
| 3. C2×#11763736 | C2 | semidirect |
| 4. C2×#11763721 | C2 | semidirect |
| 5. C2×#11763696 | C2 | semidirect |
| 10. D8×#595 | C22 | semidirect |
| 14. #11763736 | C22 | semidirect |
| 15. #11763721 | C22 | semidirect |
| 16. #11763696 | C22 | semidirect |
| 18. C2×D272 | C4 | semidirect |
| 19. C2×#10587497 | C4 | semidirect |
| 20. D16×D17 | C4 | semidirect |
| 23. C2×C17×D16 | C4 | semidirect |
| 32. C2×D8×C17 | C2×C4 | semidirect |
| 36. D8×D17 | C2×C4 | semidirect |
| 38. C2×D136 | C2×C4 | semidirect |
| 48. C17×D16 | C2×C4 | semidirect |
| 49. C2×C16×C17 | C2×C4 | semidirect |
| 50. #10587497 | C2×C4 | semidirect |
| 51. C2×#63214 | C2×C4 | semidirect |
| 52. D272 | C2×C4 | semidirect |
| 53. C16×D17 | C2×C4 | semidirect |
| 77. D8×C17 | C22×C4 | semidirect |
| 83. D136 | C22×C4 | semidirect |
| 89. C16×C17 | C22×C4 | semidirect |
| 90. #63214 | C22×C4 | semidirect |
| 150. C2×D16 | #595 | semidirect |
| 162. C2×C17 | #2177 | semidirect |
| 165. D17 | #2177 | semidirect |
| 175. C2×D8 | C2×#595 | semidirect |
| 185. D16 | C2×#595 | semidirect |
| 192. C2×C16 | C2×#595 | semidirect |
| 198. C17 | C2×#2177 | semidirect |
| 217. D8 | C22×#595 | semidirect |
| 234. C16 | C22×#595 | semidirect |
| 285. C2 | #14545182 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#595 | 2 |
| #14545182 | 2 |
| C2×#11763736 | 2 |
| C2×#11763721 | 2 |
| C2×#11763696 | 2 |
| C2×D16×D17 | 2 |
| C2×#2177 | 17 |