Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1692 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 1692 conjugacy classes of subgroups — too many to draw. Only its 361 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. C2×C32×C4⋊Q8 | C2 | semidirect |
| 2. C22×#3756 | C2 | semidirect |
| 5. #10592785 | C2 | direct (N × H) |
| 6. C2×#63630 | C2 | semidirect |
| 12. C32×C4⋊Q8 | C22 | semidirect |
| 16. C2×#3756 | C22 | semidirect |
| 23. #63630 | C22 | semidirect |
| 24. C2×C3×C4⋊Q8 | D3 | semidirect |
| 58. C3×C4⋊Q8 | C2×D3 | semidirect |
| 93. C2×C4⋊Q8 | C3⋊D3 | semidirect |
| 140. C4⋊Q8 | C2×C3⋊D3 | semidirect |
| 168. C2×C32 | #497 | semidirect |
| 206. C32 | C2×#497 | semidirect |
| 228. C2×C3 | #5086 | semidirect |
| 243. C3 | C2×#5086 | semidirect |
| 245. C2 | #10592785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊Q8 | 2 |
| C22×#3756 | 2 |
| C22×#3755 | 2 |
| C2×#64084 | 2 |
| #10592785 | 2 |
| C2×#63630 | 2 |
| C2×#5086 | 3 |