Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C113 |
| prime radical | C22×D4×C113 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C113×#1834 | C2 | semidirect |
| 4. C113×#1296 | C2 | semidirect |
| 5. C113×#1277 | C2 | semidirect |
| 112. #10621 | C113 | direct (N × H) |
| 120. #1834 | C2×C113 | semidirect |
| 122. #1296 | C2×C113 | semidirect |
| 123. #1277 | C2×C113 | semidirect |
| 124. C113 | #10621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#1954 | 2 |
| C113×#1834 | 2 |
| C113×#1802 | 2 |
| C113×#1296 | 2 |
| C113×#1277 | 2 |
| #10621 | 113 |