Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22577843 | C2 | semidirect |
| 3. #22577787 | C2 | semidirect |
| 4. #22577224 | C2 | semidirect |
| 5. #22577218 | C2 | semidirect |
| 6. #22577215 | C2 | semidirect |
| 7. #443×C137 | C2 | semidirect |
| 74. C137 | #2212 | semidirect |
| 79. #443 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577843 | 2 |
| #22577838 | 2 |
| #22577787 | 2 |
| #22577224 | 2 |
| #22577218 | 2 |
| #22577215 | 2 |
| #443×C137 | 2 |
| #2212 | 137 |