Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041332 | C2 | semidirect |
| 2. #26041332 | C2 | semidirect |
| 3. D4⋊#13089678 | C2 | semidirect |
| 6. C4⋊#13089678 | C22 | semidirect |
| 10. C4×#13089678 | C22 | semidirect |
| 25. C2×D4×C181 | C8 | semidirect |
| 87. C181 | #1478 | semidirect |
| 111. C2×D4 | #13089678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041332 | 2 |
| D4⋊#13089678 | 2 |
| C2×C4×D4×C181 | 2 |
| #1478 | 181 |