Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
636 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. C4×#63626 | C2 | semidirect |
| 3. #11773045 | C2 | semidirect |
| 4. #11772911 | C2 | semidirect |
| 5. #11772908 | C2 | semidirect |
| 6. #11772661 | C2 | semidirect |
| 7. C32×C4×D16 | C2 | semidirect |
| 16. #10589385 | C4 | semidirect |
| 21. C3×C4×D16 | D3 | semidirect |
| 33. C32×D16 | C2×C4 | semidirect |
| 42. #63626 | C2×C4 | semidirect |
| 44. C3⋊(C3⋊C32) | C2×C4 | semidirect |
| 78. C4×D16 | C3⋊D3 | semidirect |
| 88. C3×D16 | C4×D3 | semidirect |
| 166. D16 | C4×C3⋊D3 | semidirect |
| 228. C32 | #13654 | semidirect |
| 263. C3 | #10715788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10589385 | 2 |
| C4×#63626 | 2 |
| #11773045 | 2 |
| #11772911 | 2 |
| #11772908 | 2 |
| #11772661 | 2 |
| C32×C4×D16 | 2 |
| #10715788 | 3 |