Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
408 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 159 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. #11772661 | C2 | semidirect |
| 2. #11772234 | C2 | semidirect |
| 18. C32×D16 | C8 | semidirect |
| 53. C3×D16 | C3⋊C8 | semidirect |
| 105. D16 | C3⋊(C3⋊C8) | semidirect |
| 151. C32 | #7385 | semidirect |
| 177. C3 | #10682643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11772661 | 2 |
| #11772234 | 2 |
| C32×C4×D16 | 2 |
| #10682643 | 3 |