Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
719 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 719 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×SL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)×Dic6 | C2 | semidirect |
| 4. D3×Q82 | C3 | semidirect |
| 10. C3×Q82 | C2×C3 | semidirect |
| 16. Q8×Dic6 | C2×C3 | semidirect |
| 19. Q8×SL(2,𝔽3) | D3 | direct (N × H) |
| 26. D3×SL(2,𝔽3) | Q8 | direct (N × H) |
| 58. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 62. Q82 | C3×D3 | semidirect |
| 76. D3×Q8 | SL(2,𝔽3) | direct (N × H) |
| 77. D3×Q8 | C3×Q8 | semidirect |
| 129. C3×Q8 | C2×SL(2,𝔽3) | semidirect |
| 130. C3×Q8 | C2×C3×Q8 | semidirect |
| 148. Dic6 | C2×SL(2,𝔽3) | semidirect |
| 150. SL(2,𝔽3) | D3×Q8 | direct (N × H) |
| 205. Q8 | D3×SL(2,𝔽3) | direct (N × H) |
| 206. Q8 | C3×D3×Q8 | semidirect |
| 227. D3 | Q8×SL(2,𝔽3) | direct (N × H) |
| 241. C3 | C2×Q8×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×SL(2,𝔽3) | 2 |
| C4×D3×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic6 | 2 |
| D3×Q82 | 3 |
| C2×Q8×SL(2,𝔽3) | 3 |
| C2×C3×D3×Q8 | 4 |