Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19153839 | C2 | semidirect |
| 2. C2×#19153838 | C2 | semidirect |
| 3. #26041931 | C2 | semidirect |
| 4. #26041657 | C2 | semidirect |
| 5. #26041521 | C2 | semidirect |
| 6. #26041483 | C2 | semidirect |
| 7. #26041444 | C2 | semidirect |
| 8. #26041439 | C2 | semidirect |
| 9. #26041361 | C2 | semidirect |
| 10. C8×C22⋊D181 | C2 | semidirect |
| 11. #467×C181 | C2 | semidirect |
| 58. D1448 | D4 | semidirect |
| 129. Dic181 | #135 | semidirect |
| 136. C181 | #3283 | semidirect |
| 143. #467 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153838 | 2 |
| #26041931 | 2 |
| #26041657 | 2 |
| #26041521 | 2 |
| #26041483 | 2 |
| #26041444 | 2 |
| #26041439 | 2 |
| #26041361 | 2 |
| C8×C22⋊D181 | 2 |
| #467×C181 | 2 |
| #3283 | 181 |