Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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×#19153891 | C2 | semidirect |
| 2. C2×#19153884 | C2 | semidirect |
| 3. #26042196 | C2 | direct (N × H) |
| 7. #19153891 | C22 | semidirect |
| 10. #19153884 | C22 | semidirect |
| 14. #19153839 | C4 | semidirect |
| 17. C2×D1448 | C4 | semidirect |
| 19. C2×Q16×C181 | C4 | semidirect |
| 35. D1448 | C2×C4 | semidirect |
| 43. Q16×C181 | C2×C4 | semidirect |
| 80. C2×C181 | #360 | semidirect |
| 85. C181 | C2×#360 | semidirect |
| 96. C2×Q16 | #10624382 | semidirect |
| 117. Q16 | C2×#10624382 | semidirect |
| 169. C2 | #26042196 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153891 | 2 |
| C2×#19153884 | 2 |
| #26042196 | 2 |
| C2×#19153839 | 2 |
| C2×#360 | 181 |