Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041994 | C2 | semidirect |
| 2. #26041934 | C2 | semidirect |
| 3. #26041677 | C2 | semidirect |
| 4. #26041602 | C2 | semidirect |
| 5. #26041596 | C2 | semidirect |
| 6. #26041569 | C2 | semidirect |
| 7. #26041559 | C2 | semidirect |
| 8. #26041529 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041320 | C2 | semidirect |
| 11. C4×D8×C181 | C2 | semidirect |
| 101. C8×C181 | #41 | semidirect |
| 127. C181 | #3354 | semidirect |
| 137. C4×D8 | D181 | semidirect |
| 229. C8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041934 | 2 |
| #26041677 | 2 |
| #26041602 | 2 |
| #26041596 | 2 |
| #26041569 | 2 |
| #26041559 | 2 |
| #26041529 | 2 |
| #26041358 | 2 |
| #26041320 | 2 |
| C4×D8×C181 | 2 |
| #3354 | 181 |