Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#19153895 | C2 | semidirect |
| 2. #26042260 | C2 | direct (N × H) |
| 3. C2×#19153875 | C2 | semidirect |
| 6. #19153895 | C22 | semidirect |
| 10. #19153875 | C22 | semidirect |
| 14. C2×#15668450 | C4 | semidirect |
| 16. C22×D724 | C4 | semidirect |
| 18. C22×C4×D181 | C4 | semidirect |
| 20. C22×Q8×C181 | C4 | semidirect |
| 37. C2×D724 | C2×C4 | semidirect |
| 44. C2×C4×D181 | C2×C4 | semidirect |
| 51. C2×Q8×C181 | C2×C4 | semidirect |
| 107. C2×C181 | #410 | semidirect |
| 112. C181 | C2×#410 | semidirect |
| 123. C22×Q8 | #10624382 | semidirect |
| 142. C2×Q8 | C2×#10624382 | semidirect |
| 223. C2 | #26042260 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| #26042260 | 2 |
| C2×#19153875 | 2 |
| C22×#15668450 | 2 |
| C2×#410 | 181 |