Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 286 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 | C22 | C22×C16×C113 |
| Frattini, cosocle | C22×C8 | C23×C113 |
| socle, prime radical | C23×C113 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C42×C113 | C16 | semidirect |
| 44. C4×C113 | C4⋊C16 | semidirect |
| 47. #12898 | C113 | direct (N × H) |
| 53. C113 | #12898 | direct (N × H) |
| 76. C42 | C16×C113 | semidirect |
| 95. C4 | C4⋊C16×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C16×C113 | 2 |
| C42×C8×C113 | 2 |
| #12898 | 113 |