Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
282 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 166 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 | C2×D8 |
| commutator | C2×C8 | C22×C4×C113 |
| Frattini, cosocle | C22×C8 | C23×C113 |
| socle | C22×C113 | C2×#107 |
| prime radical | C23×C113 | C2×Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ C2×C4×C8×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 60. #12891 | C113 | direct (N × H) |
| 67. C113 | #12891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C16×C113 | 2 |
| C113×#1848 | 2 |
| C113×#1381 | 2 |
| #12891 | 113 |