Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
252 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C113 | #117 |
| commutator | C2×C4 | C22×C4×C113 |
| Frattini, cosocle | C22×C4 | C23×C113 |
| socle | C2×C113 | #380 |
| prime radical | C2×#41×C113 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C113 ◁ C2×M16×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#108×C113 | C2 | semidirect |
| 4. #338×C113 | C2 | semidirect |
| 61. #1813 | C113 | direct (N × H) |
| 62. C113 | #1813 | direct (N × H) |
| 64. C2×#108 | C2×C113 | semidirect |
| 66. #338 | C2×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C113 | 2 |
| C2×#108×C113 | 2 |
| #413×C113 | 2 |
| #338×C113 | 2 |
| #1813 | 113 |