Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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×#16863236 | C2 | semidirect |
| 4. C4⋊(C67⋊C32) | C2 | semidirect |
| 5. #22558389 | C2 | semidirect |
| 7. C4×Q32×C67 | C2 | semidirect |
| 97. C4×Q32 | D67 | semidirect |
| 101. C67 | #13690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863236 | 2 |
| C2×#16863233 | 2 |
| #22562470 | 2 |
| C4⋊(C67⋊C32) | 2 |
| #22558389 | 2 |
| #22558386 | 2 |
| C4×Q32×C67 | 2 |
| #13690 | 67 |