Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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. D8×#10624382 | C2 | semidirect |
| 2. #26042206 | C2 | semidirect |
| 3. #26042191 | C2 | semidirect |
| 4. #26042166 | C2 | semidirect |
| 12. D2896 | C4 | semidirect |
| 13. #19153757 | C4 | semidirect |
| 15. D16×C181 | C4 | semidirect |
| 23. D1448 | C2×C4 | semidirect |
| 26. #15668424 | C2×C4 | semidirect |
| 27. D8×C181 | C2×C4 | semidirect |
| 28. C16×C181 | C2×C4 | semidirect |
| 53. C181 | #2177 | semidirect |
| 64. D16 | #10624382 | semidirect |
| 74. D8 | C2×#10624382 | semidirect |
| 82. C16 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#10624382 | 2 |
| #26042206 | 2 |
| #26042191 | 2 |
| #26042166 | 2 |
| D16×D181 | 2 |
| #2177 | 181 |