Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D113 |
| commutator, socle, cosocle | C22×C113 | C25 |
| Fitting | #564×C113 | C2 |
| hypercenter | #564 | D113 |
| hypocenter | C113 | #3567 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20299346 | C2 | semidirect |
| 2. #20299301 | C2 | semidirect |
| 3. #20299280 | C2 | semidirect |
| 4. #20299204 | C2 | semidirect |
| 5. #20299196 | C2 | semidirect |
| 6. #20299133 | C2 | semidirect |
| 7. #564×C113 | C2 | semidirect |
| 100. C113 | #3567 | semidirect |
| 101. #564 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299346 | 2 |
| #20299301 | 2 |
| #20299280 | 2 |
| #20299204 | 2 |
| #20299196 | 2 |
| #20299133 | 2 |
| #564×C113 | 2 |
| #3567 | 113 |