Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
198 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16×C113 | C2×D4 |
| commutator | C4 | C22×C16×C113 |
| Frattini, cosocle | C2×C16 | C23×C113 |
| socle | C2×C113 | C2×C4⋊C16 |
| prime radical | C23×C113 | M32 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C113 ◁ C22×C16×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C113×#1422 | C2 | semidirect |
| 55. #13630 | C113 | direct (N × H) |
| 61. #1422 | C2×C113 | semidirect |
| 62. C113 | #13630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M64×C113 | 2 |
| C113×#2108 | 2 |
| C113×#1422 | 2 |
| #13630 | 113 |