Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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. #14544999 | C2 | semidirect |
| 4. #14544593 | C2 | semidirect |
| 5. #14543856 | C2 | semidirect |
| 6. #14543850 | C2 | semidirect |
| 12. #11763850 | C4 | semidirect |
| 13. #11763850 | C4 | semidirect |
| 19. #11763721 | C4 | semidirect |
| 26. #11762623 | C4 | semidirect |
| 27. #11762622 | C4 | semidirect |
| 28. #11762621 | C4 | semidirect |
| 29. C17×#361 | C4 | semidirect |
| 53. #10587534 | C2×C4 | semidirect |
| 64. #10587529 | C2×C4 | semidirect |
| 65. C17×M32 | C2×C4 | semidirect |
| 66. C17×#108 | C2×C4 | semidirect |
| 68. #10587490 | C2×C4 | semidirect |
| 69. #10587483 | C2×C4 | semidirect |
| 198. #361 | #595 | semidirect |
| 233. M32 | C2×#595 | semidirect |
| 238. #108 | C2×#595 | semidirect |
| 251. 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 |
| #14545093 | 2 |
| #14544999 | 2 |
| #14544593 | 2 |
| #14543856 | 2 |
| #14543850 | 2 |
| D17×#361 | 2 |
| #12647 | 17 |