Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C4×#15668449 | C2 | semidirect |
| 3. C4×Dic724 | C2 | semidirect |
| 4. C4×#15668438 | C2 | semidirect |
| 5. C4×D1448 | C2 | semidirect |
| 6. #26041317 | C2 | semidirect |
| 7. #26041276 | C2 | semidirect |
| 8. C2×C4×C8×C181 | C2 | semidirect |
| 10. #19153838 | C4 | direct (N × H) |
| 30. #15668449 | C2×C4 | semidirect |
| 36. Dic724 | C2×C4 | semidirect |
| 37. #15668438 | C2×C4 | semidirect |
| 38. D1448 | C2×C4 | semidirect |
| 48. C2×C8×C181 | C2×C4 | semidirect |
| 83. C4×C181 | #135 | semidirect |
| 92. C181 | C4×#135 | semidirect |
| 101. C2×C4×C8 | D181 | semidirect |
| 135. C2×C8 | C4×D181 | semidirect |
| 178. C4 | #19153838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| C4×#15668449 | 2 |
| C4×Dic724 | 2 |
| C4×#15668438 | 2 |
| C4×D1448 | 2 |
| #26041317 | 2 |
| #26041276 | 2 |
| C2×C4×C8×C181 | 2 |
| C4×#135 | 181 |