Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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. #22578454 | C2 | semidirect |
| 2. #22578453 | C2 | semidirect |
| 3. #22578452 | C2 | semidirect |
| 4. Q8×#11764047 | C2 | semidirect |
| 34. #14555518 | Q8 | semidirect |
| 94. C137 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578454 | 2 |
| #22578453 | 2 |
| #22578452 | 2 |
| Q8×#11764047 | 2 |
| #22578410 | 2 |
| #22578407 | 2 |
| #22578368 | 2 |
| C4×#14555518 | 2 |
| #22577958 | 2 |
| #2960 | 137 |