Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1788 conjugacy classes of subgroups; only the 353 normal subgroups are shown.
This group has 1788 conjugacy classes of subgroups — too many to draw. Only its 353 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. C22×C32×D8 | C2 | semidirect |
| 2. C2×#64147 | C2 | semidirect |
| 3. C22×#3743 | C2 | semidirect |
| 4. C2×#63659 | C2 | semidirect |
| 5. #10592858 | C2 | direct (N × H) |
| 6. C2×#63644 | C2 | semidirect |
| 12. C2×C32×D8 | C22 | semidirect |
| 16. #64147 | C22 | semidirect |
| 20. C2×#3743 | C22 | semidirect |
| 21. #63659 | C22 | semidirect |
| 22. #63644 | C22 | semidirect |
| 23. C22×C3×D8 | D3 | semidirect |
| 45. C2×C32×C8 | D4 | semidirect |
| 58. C2×C3×D8 | C2×D3 | semidirect |
| 92. C32×C8 | C2×D4 | semidirect |
| 94. C22×D8 | C3⋊D3 | semidirect |
| 116. C2×C3×C8 | #67 | semidirect |
| 143. C2×D8 | C2×C3⋊D3 | semidirect |
| 177. C3×C8 | C2×#67 | semidirect |
| 180. C2×C32 | #469 | semidirect |
| 203. C2×C8 | #638 | semidirect |
| 223. C32 | C2×#469 | semidirect |
| 248. C8 | C2×#638 | semidirect |
| 250. C2×C3 | #5159 | semidirect |
| 269. C3 | C2×#5159 | semidirect |
| 272. C2 | #10592858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×#64147 | 2 |
| C22×#3743 | 2 |
| C2×#63659 | 2 |
| #10592858 | 2 |
| C2×#63644 | 2 |
| C2×#5159 | 3 |