Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C4×Dic724 | C2 | direct (N × H) |
| 8. C2×Dic724 | C4 | direct (N × H) |
| 27. Dic724 | C2×C4 | direct (N × H) |
| 50. C2×C4×C181 | Q16 | semidirect |
| 65. C4×C181 | C2×Q16 | semidirect |
| 70. C2×C181 | C4×Q16 | semidirect |
| 74. C181 | C2×C4×Q16 | semidirect |
| 125. C2×C4 | Dic724 | direct (N × H) |
| 142. C4 | C2×Dic724 | direct (N × H) |
| 145. C2 | C4×Dic724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C2×C4×Dic362 | 2 |
| C4×Dic724 | 2 |
| C2×#19153750 | 2 |
| C2×#19153741 | 2 |
| C2×C4×C8×C181 | 2 |
| C2×C4×Q16 | 181 |