Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
514 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C113 | #127 |
| commutator | C42 | C22×C4×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle | C22×C113 | #390 |
| prime radical | C113×#3147 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C113×#1848 | C2 | semidirect |
| 3. C113×#1492 | C2 | semidirect |
| 4. C2×#322×C113 | C2 | semidirect |
| 95. #9862 | C113 | direct (N × H) |
| 101. #1848 | C2×C113 | semidirect |
| 102. #1492 | C2×C113 | semidirect |
| 103. C2×#322 | C2×C113 | semidirect |
| 104. C113 | #9862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#3147 | 2 |
| C113×#1848 | 2 |
| C113×#1492 | 2 |
| C2×#322×C113 | 2 |
| #9862 | 113 |