Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 1. C3×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 2. C3×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. #73022 | C3 | direct (N × H) |
| 8. C4⋊GL(2,𝔽3) | C2×C3 | semidirect |
| 11. C3×C8×Q8 | D3 | semidirect |
| 13. C8×SL(2,𝔽3) | C2×C3 | semidirect |
| 39. C3×SL(2,𝔽3) | D8 | semidirect |
| 43. C8×Q8 | C3×D3 | semidirect |
| 84. C3×Q8 | D24 | semidirect |
| 98. SL(2,𝔽3) | C3×D8 | semidirect |
| 103. C3×C8 | GL(2,𝔽3) | semidirect |
| 142. Q8 | C3×D24 | semidirect |
| 153. C8 | C3×GL(2,𝔽3) | semidirect |
| 176. C3 | #73022 | 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 |
| #73022 | 3 |
| C3×#1668 | 3 |
| C2×C3×D24 | 4 |