Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22563503 | C2 | semidirect |
| 5. #22558110 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 29. #14524043 | Q8 | semidirect |
| 30. #14524040 | Q8 | semidirect |
| 201. #1303 | D67 | semidirect |
| 203. C67 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563503 | 2 |
| #22561040 | 2 |
| #22558705 | 2 |
| #22558703 | 2 |
| #22558110 | 2 |
| #22558037 | 2 |
| C67×#1303 | 2 |
| #10370 | 67 |