Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
958 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C113 | C23 |
| commutator | C23 | C22×C8×C113 |
| Frattini, cosocle | C22×C8 | C23×C113 |
| socle | C23×C113 | C22×C8 |
| prime radical | C22×#41×C113 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C16×C113 | C2 | semidirect |
| 63. #12680 | C113 | direct (N × H) |
| 68. C2×C22⋊C16 | C2×C113 | semidirect |
| 69. C113 | #12680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131×C113 | 2 |
| C2×C22⋊C16×C113 | 2 |
| #12680 | 113 |