Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10588606 | C2 | semidirect |
| 3. C4×#3667 | C2 | semidirect |
| 4. D4⋊(C9⋊C8) | C2 | semidirect |
| 17. C4⋊(C9⋊C8) | C22 | semidirect |
| 20. C4×C9⋊C8 | C22 | semidirect |
| 70. D4×C9 | M16 | semidirect |
| 207. C9 | #1490 | semidirect |
| 215. D4 | #3667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C9 | 2 |
| #10588606 | 2 |
| C4×#3667 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #71599 | 3 |