Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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×#11763700 | C2 | semidirect |
| 4. #14544591 | C2 | semidirect |
| 5. #14543855 | C2 | semidirect |
| 6. #14543849 | C2 | semidirect |
| 11. #11763850 | C4 | semidirect |
| 17. #11763727 | C4 | semidirect |
| 23. #11762611 | C4 | semidirect |
| 24. #11762610 | C4 | semidirect |
| 25. #11762609 | C4 | semidirect |
| 26. C17×#357 | C4 | semidirect |
| 50. #10587535 | C2×C4 | semidirect |
| 56. #10587530 | 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 |
| 191. #357 | #595 | semidirect |
| 225. C2×C16 | C2×#595 | semidirect |
| 229. #107 | C2×#595 | semidirect |
| 238. C17 | #12647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763850 | 2 |
| C2×#11763727 | 2 |
| C2×#11763700 | 2 |
| #14544591 | 2 |
| #14543855 | 2 |
| #14543849 | 2 |
| #14530498 | 2 |
| #12647 | 17 |