Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
581 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 8. C2×C4×C3⋊Dic3 | C4 | semidirect |
| 13. C3×C3⋊#95 | C4 | semidirect |
| 15. C3×#830 | C4 | semidirect |
| 60. C3⋊#95 | Dic3 | semidirect |
| 62. #830 | Dic3 | semidirect |
| 293. C32 | #1284 | semidirect |
| 353. C3 | #67628 | semidirect |
| 354. C3 | #67682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3757 | 2 |
| C3×#5211 | 2 |
| C3×#5207 | 2 |
| #67682 | 3 |
| #67628 | 3 |