Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041990 | C2 | semidirect |
| 2. #26041680 | C2 | semidirect |
| 3. #26041582 | C2 | semidirect |
| 4. #26041566 | C2 | semidirect |
| 5. C8×Dic362 | C2 | semidirect |
| 8. #500×C181 | C2 | semidirect |
| 32. D1448 | Q8 | semidirect |
| 81. C181 | #3380 | semidirect |
| 84. #500 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| #26041680 | 2 |
| #26041582 | 2 |
| #26041566 | 2 |
| C8×Dic362 | 2 |
| C4×D1448 | 2 |
| #26041361 | 2 |
| #500×C181 | 2 |
| #3380 | 181 |