Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1606 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 287 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 |
|---|---|---|
| 3. C22×#3777 | C2 | semidirect |
| 4. #10593568 | C2 | direct (N × H) |
| 5. C2×#63747 | C2 | semidirect |
| 8. C23×#157 | C4 | semidirect |
| 16. C2×#3777 | C22 | semidirect |
| 17. #63747 | C22 | semidirect |
| 35. C22×#157 | C2×C4 | semidirect |
| 45. C23×C32 | C4⋊C4 | semidirect |
| 55. C22×C3⋊D3 | C4⋊C4 | semidirect |
| 56. C22×C3⋊D3 | C4⋊C4 | semidirect |
| 73. C2×#157 | C22⋊C4 | semidirect |
| 94. C22×C32 | C2×C4⋊C4 | semidirect |
| 105. C2×C3⋊D3 | C2×C4⋊C4 | semidirect |
| 115. #157 | C2×C22⋊C4 | semidirect |
| 151. C2×C32 | #380 | semidirect |
| 155. C3⋊D3 | #380 | semidirect |
| 205. C32 | C2×#380 | semidirect |
| 225. C23 | #3777 | semidirect |
| 267. C22 | C2×#3777 | semidirect |
| 280. C2 | #10593568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#157 | 2 |
| C22×C22⋊#157 | 2 |
| C22×#3777 | 2 |
| #10593568 | 2 |
| C2×#63747 | 2 |
| C2×#380 | 9 |