Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
456 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 162 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×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C43×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 96. C4×C113 | #330 | semidirect |
| 97. #8580 | C113 | direct (N × H) |
| 107. C113 | #8580 | direct (N × H) |
| 199. C4 | #330×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#125×C113 | 2 |
| C113×#1767 | 2 |
| C2×#330×C113 | 2 |
| C113×#1295 | 2 |
| #8580 | 113 |