Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C113 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C113 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 74. #2099 | C113 | direct (N × H) |
| 75. C113 | #2099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #389×C113 | 2 |
| #384×C113 | 2 |
| #340×C113 | 2 |
| #336×C113 | 2 |
| #2099 | 113 |