Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1459 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1459 conjugacy classes of subgroups — too many to draw. Only its 221 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. C22⋊C4×PSU(3,𝔽2) | C2 | semidirect |
| 3. #11791859 | C2 | semidirect |
| 6. C23×PSU(3,𝔽2) | C4 | semidirect |
| 9. C2×C22⋊PSU(3,𝔽2) | C4 | semidirect |
| 13. C2×C4⋊PSU(3,𝔽2) | C4 | semidirect |
| 15. C2×C4×PSU(3,𝔽2) | C4 | semidirect |
| 60. C32×#99 | Q8 | semidirect |
| 61. #63661 | Q8 | semidirect |
| 62. #63633 | Q8 | semidirect |
| 111. C32×C22⋊C4 | C2×Q8 | semidirect |
| 112. #3757 | C2×Q8 | semidirect |
| 124. C23×C32 | C4×Q8 | semidirect |
| 132. C22×C3⋊D3 | C4×Q8 | semidirect |
| 158. PSU(3,𝔽2) | #99 | direct (N × H) |
| 161. C2×C32×C4 | C4×Q8 | semidirect |
| 165. C2×C3⋊Dic3 | C4×Q8 | semidirect |
| 267. #99 | PSU(3,𝔽2) | direct (N × H) |
| 349. C22⋊C4 | C2×PSU(3,𝔽2) | semidirect |
| 376. C32 | Q8×#99 | semidirect |
| 388. C23 | C4×PSU(3,𝔽2) | semidirect |
| 423. C2×C4 | C4×PSU(3,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×PSU(3,𝔽2) | 2 |
| C22⋊C4×PSU(3,𝔽2) | 2 |
| #11791859 | 2 |
| #11785105 | 2 |
| #99×#157 | 2 |
| Q8×#99 | 9 |