Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
296 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 77 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⋊(SL(2,𝔽3)⋊C8) | C2 | semidirect |
| 16. C3×#41⋊C3 | C8 | semidirect |
| 41. C3×SL(2,𝔽3) | C2×C8 | semidirect |
| 49. C3×#41 | C3⋊C8 | semidirect |
| 55. #41⋊C3 | C3⋊C8 | semidirect |
| 106. SL(2,𝔽3) | C2×C3⋊C8 | semidirect |
| 114. #41 | C3⋊(C3⋊C8) | semidirect |
| 186. C3 | #73071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41⋊C3 | 2 |
| C3⋊(SL(2,𝔽3)⋊C8) | 2 |
| #73071 | 3 |
| #71639 | 3 |
| C4⋊(C3⋊(C3⋊C8)) | 4 |