Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. C22×C4⋊#10624382 | C2 | semidirect |
| 2. C2×#19153878 | C2 | semidirect |
| 3. D181⋊(C22⋊C8) | C2 | semidirect |
| 4. #26042152 | C2 | semidirect |
| 17. #19153791 | C4 | semidirect |
| 18. #19153790 | C4 | semidirect |
| 21. #19153787 | C4 | semidirect |
| 24. #121×C181 | C4 | semidirect |
| 34. C4⋊#10624382 | D4 | semidirect |
| 38. C2×D724 | C2×C4 | semidirect |
| 54. C4⋊Dic181 | C2×C4 | semidirect |
| 60. C2×D4×C181 | C2×C4 | semidirect |
| 62. C4⋊C4×C181 | C2×C4 | semidirect |
| 114. C22×C181 | #102 | semidirect |
| 129. C2×D181 | #102 | semidirect |
| 154. C181 | #1874 | semidirect |
| 171. #121 | #10624382 | semidirect |
| 192. C2×D4 | C2×#10624382 | semidirect |
| 214. C4⋊C4 | C2×#10624382 | semidirect |
| 289. C22 | #19153878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10624382 | 2 |
| C2×#19153878 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042152 | 2 |
| #121×D181 | 2 |
| #1874 | 181 |