Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #22560992 | C2 | semidirect |
| 5. #22558317 | C2 | semidirect |
| 6. #22558297 | C2 | semidirect |
| 7. C2×#366×C67 | C2 | semidirect |
| 18. #16863204 | C4 | semidirect |
| 46. #14523979 | C2×C4 | semidirect |
| 58. C2×C16×C67 | C2×C4 | semidirect |
| 161. C2×#366 | D67 | semidirect |
| 167. C67 | #12945 | semidirect |
| 210. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569083 | 2 |
| C2×#16863204 | 2 |
| #22561919 | 2 |
| #22560992 | 2 |
| #22558317 | 2 |
| #22558297 | 2 |
| C2×#366×C67 | 2 |
| #12945 | 67 |