Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19153849 | C2 | semidirect |
| 2. C2×#19153847 | C2 | semidirect |
| 3. C2×#19153846 | C2 | semidirect |
| 5. C2×#19153814 | C2 | semidirect |
| 6. #26041672 | C2 | semidirect |
| 7. #26041670 | C2 | semidirect |
| 8. #26041657 | C2 | semidirect |
| 9. #26041650 | C2 | semidirect |
| 10. M16×Dic181 | C2 | semidirect |
| 11. C2×#137×C181 | C2 | semidirect |
| 62. #15668433 | D4 | semidirect |
| 86. M16×C181 | D4 | semidirect |
| 140. Dic181 | #137 | semidirect |
| 146. C181 | #3152 | semidirect |
| 151. C2×#137 | D181 | semidirect |
| 224. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153847 | 2 |
| C2×#19153846 | 2 |
| #26041825 | 2 |
| C2×#19153814 | 2 |
| #26041672 | 2 |
| #26041670 | 2 |
| #26041657 | 2 |
| #26041650 | 2 |
| M16×Dic181 | 2 |
| C2×#137×C181 | 2 |
| #3152 | 181 |