Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
1318 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1318 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, socle | C23×C113 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C113 |
| Frattini, cosocle | C23×C4 | C23×C113 |
| prime radical | C24×C113 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 74. C2×C4×C113 | #101 | semidirect |
| 93. #10983 | C113 | direct (N × H) |
| 101. C113 | #10983 | direct (N × H) |
| 172. C2×C4 | #101×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Q8×C113 | 2 |
| C22×#101×C113 | 2 |
| C113×#1728 | 2 |
| #10983 | 113 |