Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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. #22578427 | C2 | semidirect |
| 2. #22578420 | C2 | semidirect |
| 3. #22578419 | C2 | semidirect |
| 4. #22578410 | C2 | semidirect |
| 6. C4×#14555520 | C2 | semidirect |
| 7. C4×#14555518 | C2 | semidirect |
| 104. C137 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578427 | 2 |
| #22578420 | 2 |
| #22578419 | 2 |
| #22578410 | 2 |
| #22578377 | 2 |
| C4×#14555520 | 2 |
| C4×#14555518 | 2 |
| C4×#14555509 | 2 |
| #2922 | 137 |