Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 94 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. C8×D4×C9 | C2 | semidirect |
| 3. #10588370 | C2 | semidirect |
| 4. D4⋊(C9⋊C8) | C2 | semidirect |
| 5. #10588162 | C2 | semidirect |
| 6. #10588156 | C2 | semidirect |
| 7. #10588132 | C2 | semidirect |
| 69. D4×C9 | M16 | semidirect |
| 83. C8×C9 | D8 | semidirect |
| 90. C8×D4 | D9 | semidirect |
| 203. C9 | #1581 | semidirect |
| 209. D4 | #3663 | semidirect |
| 225. C8 | #3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×C9 | 2 |
| C4×#3673 | 2 |
| #10588370 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588162 | 2 |
| #10588156 | 2 |
| #10588132 | 2 |
| #70841 | 3 |