Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26041933 | C2 | semidirect |
| 2. #26041682 | C2 | semidirect |
| 3. #26041592 | C2 | semidirect |
| 4. #26041590 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041556 | C2 | semidirect |
| 7. #26041513 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. C2×#19153749 | C2 | semidirect |
| 11. #547×C181 | C2 | semidirect |
| 86. #13089678 | #41 | semidirect |
| 93. D4×C181 | D8 | semidirect |
| 129. C181 | #3334 | semidirect |
| 132. #547 | D181 | semidirect |
| 216. D4 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041682 | 2 |
| #26041592 | 2 |
| #26041590 | 2 |
| #26041559 | 2 |
| #26041556 | 2 |
| #26041513 | 2 |
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| C2×#19153749 | 2 |
| #547×C181 | 2 |
| #3334 | 181 |