Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
168 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 58 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. #22578453 | C2 | semidirect |
| 3. #22578264 | C2 | semidirect |
| 4. #22578253 | C2 | semidirect |
| 6. #22578245 | C2 | semidirect |
| 45. #11764047 | SD16 | semidirect |
| 77. C137 | #1582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578453 | 2 |
| D4×#11764047 | 2 |
| #22578264 | 2 |
| #22578253 | 2 |
| D4⋊#11764047 | 2 |
| #22578245 | 2 |
| #22577494 | 2 |
| #1582 | 137 |