Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581677 | C2 | semidirect |
| 2. #22581618 | C2 | semidirect |
| 3. #22581314 | C2 | semidirect |
| 4. #22581246 | C2 | semidirect |
| 5. #22581230 | C2 | semidirect |
| 7. #22581155 | C2 | semidirect |
| 8. #22581083 | C2 | semidirect |
| 9. #22581056 | C2 | semidirect |
| 11. #487×C139 | C2 | semidirect |
| 122. C139 | #3367 | semidirect |
| 127. #487 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581677 | 2 |
| #22581618 | 2 |
| #22581314 | 2 |
| #22581246 | 2 |
| #22581230 | 2 |
| #22581171 | 2 |
| #22581155 | 2 |
| #22581083 | 2 |
| #22581056 | 2 |
| C4×D1112 | 2 |
| #487×C139 | 2 |
| #3367 | 139 |