Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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. Q8×D724 | C2 | semidirect |
| 2. #26041682 | C2 | semidirect |
| 3. #26041559 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. Q8×#13089678 | C2 | semidirect |
| 7. D4×Q8×C181 | C2 | semidirect |
| 28. #15668434 | Q8 | direct (N × H) |
| 47. D724 | C2×Q8 | semidirect |
| 51. #13089678 | C2×Q8 | semidirect |
| 54. Q8×C181 | D8 | semidirect |
| 56. D4×C181 | C2×Q8 | semidirect |
| 80. C181 | Q8×D8 | semidirect |
| 83. D4×Q8 | D181 | semidirect |
| 129. Q8 | #15668434 | direct (N × H) |
| 133. D4 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041682 | 2 |
| #26041559 | 2 |
| #26041556 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668434 | 2 |
| D4×Q8×C181 | 2 |
| Q8×D8 | 181 |