Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #26041747 | C2 | semidirect |
| 3. #26041373 | C2 | semidirect |
| 4. #26041366 | C2 | semidirect |
| 5. #26041361 | C2 | semidirect |
| 6. #26041273 | C2 | semidirect |
| 7. C2×C8×Dic181 | C2 | semidirect |
| 8. #427×C181 | C2 | semidirect |
| 10. #19153838 | C4 | semidirect |
| 30. #15668449 | C2×C4 | semidirect |
| 37. Dic724 | C2×C4 | semidirect |
| 38. #15668438 | C2×C4 | semidirect |
| 39. D1448 | C2×C4 | semidirect |
| 49. C2×C8×C181 | C2×C4 | semidirect |
| 87. Dic181 | #135 | semidirect |
| 92. C181 | C4×#135 | semidirect |
| 99. #427 | D181 | semidirect |
| 136. C2×C8 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| #26041747 | 2 |
| #26041373 | 2 |
| #26041366 | 2 |
| #26041361 | 2 |
| #26041273 | 2 |
| C2×C8×Dic181 | 2 |
| #427×C181 | 2 |
| C4×#135 | 181 |