Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #393 |
| commutator, Frattini, cosocle | C25 | C23×C113 |
| prime radical | C25×C113 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C25×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C23×C4×C113 | Q8 | semidirect |
| 66. #10391 | C113 | direct (N × H) |
| 75. C113 | #10391 | direct (N × H) |
| 83. C23×C4 | Q8×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#2840 | 2 |
| C113×#1819 | 2 |
| C113×#1304 | 2 |
| #10391 | 113 |