Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26042046 | C2 | semidirect |
| 2. #26041296 | C2 | semidirect |
| 3. #26041275 | C2 | semidirect |
| 4. #26041246 | C2 | semidirect |
| 5. #26041051 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 22. #137×C181 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C181 | C4 | semidirect |
| 118. C181 | #1881 | semidirect |
| 130. #137 | Dic181 | semidirect |
| 132. AGL(1,ℤ/8) | Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042046 | 2 |
| #26041296 | 2 |
| #26041275 | 2 |
| #26041246 | 2 |
| #26041051 | 2 |
| #26041043 | 2 |
| #575×C181 | 2 |
| #1881 | 181 |