Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Q8×Dic362 | C2 | semidirect |
| 3. #26041640 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041558 | C2 | semidirect |
| 7. #26041503 | C2 | semidirect |
| 9. #26041409 | C2 | semidirect |
| 10. #26041382 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 118. C181 | #3375 | semidirect |
| 130. C4×Q16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| Q8×Dic362 | 2 |
| #26041640 | 2 |
| #26041626 | 2 |
| #26041574 | 2 |
| #26041558 | 2 |
| #26041503 | 2 |
| #26041479 | 2 |
| #26041409 | 2 |
| #26041382 | 2 |
| C4×Q16×C181 | 2 |
| #3375 | 181 |