Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C2×C4×Q8×C113 | C2 |
| hypercenter | C2×C4×Q8 | D113 |
| hypocenter | C113 | #3497 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813670 | C2 | semidirect |
| 2. #20299270 | C2 | semidirect |
| 3. Q8×D452 | C2 | semidirect |
| 4. #20299260 | C2 | semidirect |
| 5. #20299179 | C2 | semidirect |
| 6. #20299148 | C2 | semidirect |
| 7. C2×C4×Q8×C113 | C2 | semidirect |
| 39. C2×Q8×C113 | D4 | semidirect |
| 74. C4×C113 | 2−1+4 | semidirect |
| 82. C113 | #3497 | semidirect |
| 89. C2×C4×Q8 | D113 | semidirect |
| 112. C2×Q8 | D452 | semidirect |
| 157. C4 | #16813670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813670 | 2 |
| #20299270 | 2 |
| Q8×D452 | 2 |
| #20299260 | 2 |
| #20299179 | 2 |
| #20299148 | 2 |
| C2×C4×Q8×C113 | 2 |
| #3497 | 113 |