Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10592577 | C2 | semidirect |
| 4. C3×#4490 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589133 | C2 | semidirect |
| 34. #4490 | D3 | semidirect |
| 240. C32 | #2228 | semidirect |
| 277. C3 | #69180 | semidirect |
| 278. C3 | #69354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592577 | 2 |
| #10590777 | 2 |
| C3×#4491 | 2 |
| C3×#4490 | 2 |
| #10589139 | 2 |
| #10589133 | 2 |
| #10589115 | 2 |
| #69354 | 3 |
| #69180 | 3 |