Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
344 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4⋊#13089685 | C2 | semidirect |
| 2. C2×C4×#13089685 | C2 | semidirect |
| 3. #26042127 | C2 | direct (N × H) |
| 8. C4⋊#13089685 | C22 | semidirect |
| 10. C4×#13089685 | C22 | semidirect |
| 27. C2×D724 | C8 | semidirect |
| 53. D724 | C2×C8 | semidirect |
| 88. C2×C181 | D4⋊C8 | semidirect |
| 93. C181 | C2×D4⋊C8 | semidirect |
| 183. C2 | #26042127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13089685 | 2 |
| C2×C4×#13089685 | 2 |
| #26042127 | 2 |
| C2×#19153778 | 2 |
| C2×D4⋊C8 | 181 |