Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
499 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 3. C3×#4455 | C2 | semidirect |
| 4. C3×C8×C3⋊C8 | C2 | semidirect |
| 5. #10589078 | C2 | semidirect |
| 25. #4455 | D3 | semidirect |
| 27. C8×C3⋊C8 | D3 | semidirect |
| 70. C32×C8 | M16 | semidirect |
| 73. C3×C3⋊C8 | M16 | semidirect |
| 149. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 150. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 155. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 191. C32 | #1455 | semidirect |
| 202. C8 | #3712 | semidirect |
| 220. C3 | #68050 | semidirect |
| 221. C3 | #68075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3743 | 2 |
| C4×#3712 | 2 |
| C3×#4455 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #10589078 | 2 |
| #68075 | 3 |
| #68050 | 3 |