Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
354 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 214 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 | #127 |
| commutator | C42 | C22×C4×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle | C22×C113 | #384 |
| prime radical | C23×C113 | C4⋊Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. C8×C113 | #108 | semidirect |
| 59. #8823 | C113 | direct (N × H) |
| 66. C113 | #8823 | direct (N × H) |
| 113. C8 | #108×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#1848 | 2 |
| C113×#1567 | 2 |
| C2×C82×C113 | 2 |
| #8823 | 113 |