Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 6063 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has at least 6063 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72252244 |
| commutator, cosocle | #72215518 | C22 |
| Frattini | C23×C4 | C2×#1020 |
| Fitting | #72233407 | D3 |
| hypercenter | C2×C4 | #87588⋊C2 |
| hypocenter | #11710730 | D4 |
| LCS | G ▷ #72215518 ▷ #11710730 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72233431 | C2 | semidirect |
| 2. #72233415 | C2 | semidirect |
| 3. #72233407 | D3 | semidirect |
| 4. #72218487 | C2 | semidirect |
| 8. #63076 | S4 | semidirect |
| 10. #20612 | S4 | semidirect |
| 11. #20579 | S4 | semidirect |
| 21. C22×C8 | #5934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72258446 | 3 |
| #72252250 | 4 |
| #72236877 | 4 |
| #72236783 | 4 |
| #72233431 | 2 |
| #72233415 | 2 |
| #72218487 | 2 |