Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1291 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1291 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. M16×PSU(3,𝔽2) | C2 | semidirect |
| 3. #11791887 | C2 | semidirect |
| 48. C32×#100 | Q8 | semidirect |
| 49. #63660 | Q8 | semidirect |
| 50. #63650 | Q8 | semidirect |
| 84. C32×M16 | C2×Q8 | semidirect |
| 85. #3748 | C2×Q8 | semidirect |
| 117. PSU(3,𝔽2) | #100 | direct (N × H) |
| 199. #100 | PSU(3,𝔽2) | direct (N × H) |
| 250. M16 | C2×PSU(3,𝔽2) | semidirect |
| 274. C32 | Q8×#100 | 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 |
| M16×PSU(3,𝔽2) | 2 |
| #11791887 | 2 |
| #11785132 | 2 |
| #100×#157 | 2 |
| Q8×#100 | 9 |