Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26042081 | C2 | semidirect |
| 2. #26041714 | C2 | semidirect |
| 3. C2×D2896 | C2 | semidirect |
| 4. #26041550 | C2 | semidirect |
| 5. #26041091 | C2 | semidirect |
| 6. #26041062 | C2 | semidirect |
| 7. #359×C181 | C2 | semidirect |
| 14. C2×D1448 | C22 | semidirect |
| 20. #19153756 | C22 | semidirect |
| 23. C2×C16×C181 | C22 | semidirect |
| 24. #108×C181 | C22 | semidirect |
| 93. C181 | #2192 | semidirect |
| 100. #359 | D181 | semidirect |
| 116. C2×C16 | C2×D181 | semidirect |
| 117. #108 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042081 | 2 |
| #26041714 | 2 |
| C2×D2896 | 2 |
| #26041550 | 2 |
| #26041091 | 2 |
| #26041062 | 2 |
| #359×C181 | 2 |
| #2192 | 181 |