Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
402 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C113 | C2×D4 |
| commutator | C22×C4 | C22×C4×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle, prime radical | C23×C113 | C2×C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C113 ◁ C43×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 58. #8810 | C113 | direct (N × H) |
| 66. C113 | #8810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#1842 | 2 |
| C113×#1744 | 2 |
| C2×#335×C113 | 2 |
| #8810 | 113 |