Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #22577482 | C2 | semidirect |
| 3. #22577473 | C2 | semidirect |
| 4. C8×D548 | C2 | semidirect |
| 5. #22577460 | C2 | semidirect |
| 6. #22577368 | C2 | semidirect |
| 7. #431×C137 | C2 | semidirect |
| 92. C137 | #2981 | semidirect |
| 99. #431 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577953 | 2 |
| #22577482 | 2 |
| #22577473 | 2 |
| C8×D548 | 2 |
| #22577460 | 2 |
| #22577368 | 2 |
| #431×C137 | 2 |
| #2981 | 137 |