Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
272 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C113 | C2×D4 |
| commutator | C2×C4 | C22×C4×C113 |
| Frattini, cosocle | C22×C4 | C23×C113 |
| socle | C22×C113 | C2×C4⋊C4 |
| prime radical | C24×C113 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C23×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#108×C113 | C2 | semidirect |
| 4. #341×C113 | C2 | semidirect |
| 58. #1811 | C113 | direct (N × H) |
| 59. C113 | #1811 | direct (N × H) |
| 61. C2×#108 | C2×C113 | semidirect |
| 63. #341 | C2×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C113 | 2 |
| C2×#108×C113 | 2 |
| #407×C113 | 2 |
| #341×C113 | 2 |
| #1811 | 113 |