Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×#17984176 | C2 | semidirect |
| 2. #22578437 | C2 | semidirect |
| 3. #22578433 | C2 | semidirect |
| 4. #22578431 | C2 | semidirect |
| 5. #22578404 | C2 | semidirect |
| 6. #22578378 | C2 | semidirect |
| 7. C4×#14555520 | C2 | semidirect |
| 33. #14555520 | D4 | semidirect |
| 93. C4×C137 | #131 | semidirect |
| 103. C137 | #2935 | semidirect |
| 201. C4 | #17984176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984176 | 2 |
| #22578437 | 2 |
| #22578433 | 2 |
| #22578431 | 2 |
| #22578404 | 2 |
| #22578378 | 2 |
| C4×#14555520 | 2 |
| #22577954 | 2 |
| #2935 | 137 |