Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 241 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. #26041410 | C2 | semidirect |
| 2. Q8×#13089678 | C2 | semidirect |
| 20. #15668433 | Q8 | direct (N × H) |
| 37. #13089678 | C2×Q8 | semidirect |
| 40. Q8×C181 | M16 | semidirect |
| 66. C181 | Q8×M16 | semidirect |
| 105. Q8 | #15668433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041410 | 2 |
| Q8×#13089678 | 2 |
| #26041303 | 2 |
| C4×#15668433 | 2 |
| C2×C4×Q8×C181 | 2 |
| Q8×M16 | 181 |