Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C113 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C113 |
| prime radical | C24×C113 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #400×C113 | C2 | semidirect |
| 4. #395×C113 | C2 | semidirect |
| 59. #2817 | C113 | direct (N × H) |
| 60. C113 | #2817 | direct (N × H) |
| 62. #400 | C2×C113 | semidirect |
| 64. #395 | C2×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C113 | 2 |
| #400×C113 | 2 |
| #397×C113 | 2 |
| #395×C113 | 2 |
| #381×C113 | 2 |
| #2817 | 113 |