Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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×#19153884 | C2 | semidirect |
| 2. C2×#19153878 | C2 | semidirect |
| 3. C2×#19153870 | C2 | semidirect |
| 4. #26042231 | C2 | semidirect |
| 14. C2×D1448 | C4 | semidirect |
| 15. C2×#15668434 | C4 | semidirect |
| 19. C2×D8×C181 | C4 | semidirect |
| 66. #13089678 | C22⋊C4 | semidirect |
| 71. C8×C181 | C22⋊C4 | semidirect |
| 95. C181 | #1972 | semidirect |
| 107. C2×D8 | #10624382 | semidirect |
| 167. C8 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153884 | 2 |
| C2×#19153878 | 2 |
| C2×#19153870 | 2 |
| #26042231 | 2 |
| C2×D8×D181 | 2 |
| #1972 | 181 |