Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
258 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #117 |
| commutator | C22×C4 | C22×C4×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle | C22×C113 | #383 |
| prime radical | C23×C113 | #117 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C2×#97×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 51. #8802 | C113 | direct (N × H) |
| 59. C113 | #8802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#1745 | 2 |
| C113×#1281 | 2 |
| C113×#1276 | 2 |
| C113×#1275 | 2 |
| #8802 | 113 |