Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26041910 | C2 | semidirect |
| 4. #26041040 | C2 | semidirect |
| 5. #343×C181 | C2 | semidirect |
| 22. C2×D724 | Q8 | semidirect |
| 81. C181 | #2027 | semidirect |
| 86. #343 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041910 | 2 |
| #26041285 | 2 |
| #26041180 | 2 |
| #26041040 | 2 |
| #343×C181 | 2 |
| #2027 | 181 |