Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2434 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 2434 conjugacy classes of subgroups — too many to draw. Only its 258 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. C22×C4⋊#157 | C2 | semidirect |
| 3. C22×#3787 | C2 | semidirect |
| 4. C2×#63782 | C2 | direct (N × H) |
| 7. C22×C32×D4 | C4 | semidirect |
| 11. C2×D4×C3⋊D3 | C4 | semidirect |
| 13. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 17. C2×C4⋊#157 | C22 | semidirect |
| 19. C2×#3787 | C22 | semidirect |
| 20. #63782 | C22 | direct (N × H) |
| 32. C2×C32×D4 | C2×C4 | semidirect |
| 40. D4×C3⋊D3 | C2×C4 | semidirect |
| 43. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 50. C4⋊#157 | C23 | semidirect |
| 52. #3787 | C23 | semidirect |
| 80. C32×D4 | C22×C4 | semidirect |
| 88. C4⋊(C3⋊D3) | C22×C4 | semidirect |
| 125. C22×C32 | #102 | semidirect |
| 132. C2×C3⋊D3 | #102 | semidirect |
| 149. C22×D4 | #157 | semidirect |
| 188. C2×C32 | C2×#102 | semidirect |
| 191. C3⋊D3 | C2×#102 | semidirect |
| 211. C2×D4 | C2×#157 | semidirect |
| 243. C32 | C22×#102 | semidirect |
| 263. D4 | C22×#157 | semidirect |
| 295. C22 | #63782 | direct (N × H) |
| 308. C2 | C2×#63782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C3⋊D3 | 2 |
| C22×C4⋊#157 | 2 |
| C22×#3787 | 2 |
| C2×#63782 | 2 |
| C22×#102 | 9 |