Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26042077 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041283 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041051 | C2 | semidirect |
| 7. #421×C181 | C2 | semidirect |
| 36. C2×Dic362 | D4 | semidirect |
| 43. C2×D724 | D4 | semidirect |
| 55. C2×#13089678 | D4 | semidirect |
| 70. M16×C181 | D4 | semidirect |
| 142. C181 | #2008 | semidirect |
| 147. #421 | D181 | semidirect |
| 208. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| C2×#19153844 | 2 |
| #26041843 | 2 |
| #26041283 | 2 |
| #26041252 | 2 |
| #26041051 | 2 |
| #421×C181 | 2 |
| #2008 | 181 |