Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19153839 | C2 | semidirect |
| 2. C2×#19153837 | C2 | semidirect |
| 3. C2×#19153835 | C2 | semidirect |
| 4. #26041828 | C2 | semidirect |
| 5. #26041663 | C2 | semidirect |
| 6. #26041661 | C2 | semidirect |
| 7. #26041657 | C2 | semidirect |
| 8. #26041654 | C2 | semidirect |
| 9. #26041650 | C2 | semidirect |
| 10. C4×C8×D181 | C2 | semidirect |
| 11. #495×C181 | C2 | semidirect |
| 62. C8×D181 | D4 | semidirect |
| 63. C8×D181 | D4 | semidirect |
| 119. Dic181 | #135 | semidirect |
| 125. C181 | #3147 | semidirect |
| 133. #495 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153837 | 2 |
| C2×#19153835 | 2 |
| #26041828 | 2 |
| #26041663 | 2 |
| #26041661 | 2 |
| #26041657 | 2 |
| #26041654 | 2 |
| #26041650 | 2 |
| C4×C8×D181 | 2 |
| #495×C181 | 2 |
| #3147 | 181 |