Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26042296 | C2 | semidirect |
| 2. #26042282 | C2 | semidirect |
| 3. D4⋊#13089685 | C2 | semidirect |
| 8. C4⋊#13089685 | C22 | semidirect |
| 10. C4×#13089685 | C22 | semidirect |
| 64. D4×C181 | M16 | semidirect |
| 89. C181 | #1486 | semidirect |
| 140. D4 | #15668458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042296 | 2 |
| #26042282 | 2 |
| D4⋊#13089685 | 2 |
| C2×D4×Dic181 | 2 |
| #1486 | 181 |