Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #26042347 | C2 | direct (N × H) |
| 2. C2×Q8×#10624382 | C2 | semidirect |
| 5. Q8×#10624382 | C22 | semidirect |
| 10. C22×Dic362 | C4 | semidirect |
| 11. C2×Q8×D181 | C4 | semidirect |
| 12. C2×Q8×D181 | C4 | semidirect |
| 16. C22×Q8×C181 | C4 | semidirect |
| 23. C2×Dic362 | C2×C4 | semidirect |
| 25. Q8×D181 | C2×C4 | semidirect |
| 33. C2×Q8×C181 | C2×C4 | semidirect |
| 66. C2×C181 | #519 | semidirect |
| 69. D181 | #519 | semidirect |
| 71. C181 | C2×#519 | semidirect |
| 82. C22×Q8 | #10624382 | semidirect |
| 96. C2×Q8 | C2×#10624382 | semidirect |
| 141. C2 | #26042347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042347 | 2 |
| C2×Q8×#10624382 | 2 |
| C2×#19153895 | 2 |
| C22×Q8×D181 | 2 |
| C2×#519 | 181 |