Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22577805 | C2 | semidirect |
| 2. #22577230 | C2 | semidirect |
| 3. #22577228 | C2 | semidirect |
| 4. C4⋊#14555485 | C2 | semidirect |
| 62. C137 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577805 | 2 |
| #22577230 | 2 |
| #22577228 | 2 |
| C4⋊#14555485 | 2 |
| #22577204 | 2 |
| C4×D8×C137 | 2 |
| #2228 | 137 |