Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. C2×#19153761 | C2 | direct (N × H) |
| 4. C22×C16×C181 | C2 | semidirect |
| 8. C2×Dic724 | C22 | semidirect |
| 11. #19153761 | C22 | direct (N × H) |
| 13. C2×C16×C181 | C22 | semidirect |
| 21. Dic724 | C23 | semidirect |
| 27. C16×C181 | C23 | semidirect |
| 40. C22×C181 | SD32 | semidirect |
| 47. C2×C181 | C2×SD32 | semidirect |
| 50. C181 | C22×SD32 | semidirect |
| 55. C22×C16 | D181 | semidirect |
| 64. C2×C16 | C2×D181 | semidirect |
| 78. C16 | C22×D181 | semidirect |
| 93. C22 | #19153761 | direct (N × H) |
| 99. C2 | C2×#19153761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C22×D1448 | 2 |
| C2×#19153761 | 2 |
| C22×C16×C181 | 2 |
| C22×SD32 | 181 |