Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #26041040 | C2 | semidirect |
| 5. #26041038 | C2 | semidirect |
| 6. #26041035 | C2 | semidirect |
| 7. H(3,ℤ/4)×C181 | C2 | semidirect |
| 14. #19153773 | C4 | semidirect |
| 16. C42×D181 | C4 | semidirect |
| 102. C181 | #1827 | semidirect |
| 110. H(3,ℤ/4) | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041747 | 2 |
| #26041261 | 2 |
| #26041252 | 2 |
| #26041040 | 2 |
| #26041038 | 2 |
| #26041035 | 2 |
| H(3,ℤ/4)×C181 | 2 |
| #1827 | 181 |