Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22577782 | C2 | semidirect |
| 2. #22577693 | C2 | semidirect |
| 3. #22577152 | C2 | semidirect |
| 4. D4⋊#11764040 | C2 | semidirect |
| 60. C137 | #1634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577782 | 2 |
| #22577693 | 2 |
| #22577152 | 2 |
| D4⋊#11764040 | 2 |
| #555×C137 | 2 |
| #1634 | 137 |