Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 2. C2×#19153879 | C2 | semidirect |
| 4. #26042152 | C2 | semidirect |
| 16. #19153796 | C4 | semidirect |
| 17. #19153795 | C4 | semidirect |
| 20. #19153792 | C4 | semidirect |
| 24. C22⋊Q8×C181 | C4 | semidirect |
| 37. C2×Dic362 | C2×C4 | semidirect |
| 50. C4⋊Dic181 | C2×C4 | semidirect |
| 57. C2×Q8×C181 | C2×C4 | semidirect |
| 60. C4⋊C4×C181 | C2×C4 | semidirect |
| 101. C22×C181 | #103 | semidirect |
| 109. C2×D181 | #103 | semidirect |
| 134. C181 | #1872 | semidirect |
| 150. C22⋊Q8 | #10624382 | semidirect |
| 165. C2×Q8 | C2×#10624382 | semidirect |
| 192. C4⋊C4 | C2×#10624382 | semidirect |
| 249. C22 | #19153879 | 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×#19153879 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042152 | 2 |
| C22⋊Q8×D181 | 2 |
| #1872 | 181 |