Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
324 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 119 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. #64078 | C2 | semidirect |
| 4. #63634 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 23. C32×D4 | Q8 | semidirect |
| 59. C3×D4 | Dic6 | semidirect |
| 91. C32 | #474 | semidirect |
| 95. D4 | #634 | semidirect |
| 117. C3 | #5007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| #64078 | 2 |
| #63659 | 2 |
| #63634 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #5007 | 3 |