Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 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. #26042205 | C2 | semidirect |
| 3. #26042191 | C2 | semidirect |
| 4. C16×#10624382 | 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 |
| 48. #10624382 | D16 | direct (N × H) |
| 56. C181 | C4×D16 | semidirect |
| 67. D16 | #10624382 | direct (N × H) |
| 77. D8 | C2×#10624382 | semidirect |
| 85. 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 |
| #26042205 | 2 |
| #26042191 | 2 |
| C16×#10624382 | 2 |
| D16×D181 | 2 |
| C4×D16 | 181 |