Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
900 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 242 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 |
| 2. C3×D4×SL(2,𝔽3) | C2 | semidirect |
| 3. C2×C3×C4×SL(2,𝔽3) | C2 | semidirect |
| 4. C3×Q8×#41 | C3 | semidirect |
| 5. #41×SL(2,𝔽3) | C3 | direct (N × H) |
| 10. C3×Q82 | C2×C3 | semidirect |
| 13. C3×D4×Q8 | C2×C3 | semidirect |
| 16. C2×C3×C4×Q8 | C2×C3 | semidirect |
| 17. Q8×SL(2,𝔽3) | C2×C3 | semidirect |
| 18. D4×SL(2,𝔽3) | C2×C3 | semidirect |
| 19. C2×C4×SL(2,𝔽3) | C2×C3 | semidirect |
| 26. Q8×#41 | C32 | semidirect |
| 56. C3×SL(2,𝔽3) | #41 | direct (N × H) |
| 57. Q82 | C2×C32 | semidirect |
| 60. D4×Q8 | C2×C32 | semidirect |
| 63. C2×C4×Q8 | C2×C32 | semidirect |
| 65. C3×#41 | SL(2,𝔽3) | direct (N × H) |
| 124. C3×Q8 | C2×SL(2,𝔽3) | semidirect |
| 125. C3×Q8 | C3×#41 | semidirect |
| 127. C3×D4 | C2×SL(2,𝔽3) | semidirect |
| 138. C2×C3×C4 | C2×SL(2,𝔽3) | semidirect |
| 141. SL(2,𝔽3) | C3×#41 | direct (N × H) |
| 146. #41 | C3×SL(2,𝔽3) | direct (N × H) |
| 191. Q8 | C2×C3×SL(2,𝔽3) | semidirect |
| 192. Q8 | C32×#41 | semidirect |
| 193. D4 | C2×C3×SL(2,𝔽3) | semidirect |
| 201. C2×C4 | C2×C3×SL(2,𝔽3) | semidirect |
| 224. C3 | #41×SL(2,𝔽3) | direct (N × H) |
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 |
| C3×D4×SL(2,𝔽3) | 2 |
| C2×C3×C4×SL(2,𝔽3) | 2 |
| C3×Q8×#41 | 3 |
| #41×SL(2,𝔽3) | 3 |
| C2×C32×#41 | 4 |