Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
526 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 3. C2×#11763696 | C2 | semidirect |
| 4. #107×#595 | C2 | semidirect |
| 5. #14543842 | C2 | semidirect |
| 6. #14543841 | C2 | semidirect |
| 11. D8×#595 | C4 | semidirect |
| 17. #11763721 | C4 | semidirect |
| 23. #11762611 | C4 | semidirect |
| 24. #11762610 | C4 | semidirect |
| 25. #11762609 | C4 | semidirect |
| 26. C17×#357 | C4 | semidirect |
| 52. #10587534 | C2×C4 | semidirect |
| 56. #10587529 | C2×C4 | semidirect |
| 57. C2×C16×C17 | C2×C4 | semidirect |
| 58. C17×#107 | C2×C4 | semidirect |
| 59. #10587489 | C2×C4 | semidirect |
| 60. C2×#63214 | C2×C4 | semidirect |
| 93. D8×C17 | C42 | semidirect |
| 102. D136 | C42 | semidirect |
| 204. #357 | #595 | semidirect |
| 241. C2×C16 | C2×#595 | semidirect |
| 248. #107 | C2×#595 | semidirect |
| 253. C17 | #12637 | semidirect |
| 276. D8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#595 | 2 |
| C2×#11763721 | 2 |
| C2×#11763696 | 2 |
| #107×#595 | 2 |
| #14543842 | 2 |
| #14543841 | 2 |
| D17×#357 | 2 |
| #12637 | 17 |