Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#19153904 | C2 | semidirect |
| 2. C2×#19153881 | C2 | semidirect |
| 3. C2×#19153881 | C2 | semidirect |
| 4. #26042254 | C2 | semidirect |
| 5. #26042155 | C2 | semidirect |
| 6. (C2×#10624382)⋊C8 | C2 | semidirect |
| 24. C2×#15668436 | C4 | semidirect |
| 25. C2×#15668436 | C4 | semidirect |
| 26. C2×D1448 | C4 | semidirect |
| 28. C2×Q16×C181 | C4 | semidirect |
| 130. C181 | #1876 | semidirect |
| 143. C2×Q16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153904 | 2 |
| C2×#19153881 | 2 |
| #26042254 | 2 |
| #26042155 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| C2×#19153839 | 2 |
| #1876 | 181 |