Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
245 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 48 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. C3×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C3×SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 4. #73018 | C3 | direct (N × H) |
| 11. C3×C8×Q8 | D3 | semidirect |
| 15. C8×SL(2,𝔽3) | C2×C3 | semidirect |
| 16. SL(2,𝔽3)⋊C8 | C2×C3 | semidirect |
| 51. C3×SL(2,𝔽3) | M16 | semidirect |
| 54. C8×Q8 | C3×D3 | semidirect |
| 108. C3×Q8 | ΓL(1,𝔽25) | semidirect |
| 123. SL(2,𝔽3) | C3×M16 | semidirect |
| 131. C3×C8 | GL(2,𝔽3) | semidirect |
| 176. Q8 | C3×ΓL(1,𝔽25) | semidirect |
| 190. C8 | C3×GL(2,𝔽3) | semidirect |
| 214. C3 | #73018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×GL(2,𝔽3) | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| C3×SL(2,𝔽3)⋊C8 | 2 |
| #73018 | 3 |
| C3×#1583 | 3 |
| C2×C3×ΓL(1,𝔽25) | 4 |