Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic724 | C2 | semidirect |
| 2. C2×Q16×D181 | C2 | semidirect |
| 4. #26041657 | C2 | semidirect |
| 5. #26041521 | C2 | semidirect |
| 6. #26041488 | C2 | semidirect |
| 7. #26041436 | C2 | semidirect |
| 8. #26041434 | C2 | semidirect |
| 9. #26041373 | C2 | semidirect |
| 11. #467×C181 | C2 | semidirect |
| 55. Dic724 | D4 | semidirect |
| 87. C22⋊D181 | Q16 | semidirect |
| 112. C22×C181 | C2×Q16 | semidirect |
| 116. C2×D181 | C2×Q16 | semidirect |
| 126. Dic181 | C2×Q16 | semidirect |
| 132. C181 | D4×Q16 | semidirect |
| 139. #467 | D181 | semidirect |
| 248. C22 | Q16×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C2×Q16×D181 | 2 |
| #26041942 | 2 |
| #26041657 | 2 |
| #26041521 | 2 |
| #26041488 | 2 |
| #26041436 | 2 |
| #26041434 | 2 |
| #26041373 | 2 |
| C8×C22⋊D181 | 2 |
| #467×C181 | 2 |
| D4×Q16 | 181 |