Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 6938 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has at least 6938 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72240418 |
| commutator, cosocle, hypocenter | #154044 | C22×C3 |
| Frattini, socle | C25 | C22×C22⋊A4 |
| Fitting | #72299698 | C3 |
| LCS | G ▷ #154044 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72299861 | C2 | semidirect |
| 2. #72299846 | C2 | semidirect |
| 3. #72299698 | C3 | semidirect |
| 4. #72299697 | C2×C3 | semidirect |
| 5. #72299692 | C2×C3 | semidirect |
| 6. #72210009 | C22 | semidirect |
| 28. #392 | #127⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72299861 | 2 |
| #72299846 | 2 |
| #72299828 | 4 |
| #72299818 | 4 |
| #72299814 | 4 |
| #72299803 | 4 |
| #72299698 | 3 |