Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22568191 | C2 | semidirect |
| 2. #22561444 | C2 | semidirect |
| 3. #22561296 | C2 | semidirect |
| 5. #22558033 | C2 | semidirect |
| 6. #22558029 | C2 | semidirect |
| 7. C67×#1272 | C2 | semidirect |
| 236. #1272 | D67 | semidirect |
| 239. C67 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568191 | 2 |
| #22561444 | 2 |
| #22561296 | 2 |
| #22561282 | 2 |
| #22558033 | 2 |
| #22558029 | 2 |
| C67×#1272 | 2 |
| #7746 | 67 |