Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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×#10625011 | C2 | semidirect |
| 2. C2×#10625009 | C2 | semidirect |
| 3. #13092658 | C2 | semidirect |
| 4. #13092221 | C2 | semidirect |
| 5. #13092218 | C2 | semidirect |
| 6. C22⋊(C23⋊C16) | C2 | semidirect |
| 108. C23 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625011 | 2 |
| C2×#10625009 | 2 |
| #13092658 | 2 |
| #13092221 | 2 |
| #13092218 | 2 |
| C22⋊(C23⋊C16) | 2 |
| C2×C23×#135 | 2 |
| #2189 | 23 |