Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
394 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 394 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 | C24×C113 | Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C23×C4×C113 ◁ C23×C8×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#368×C113 | C2 | semidirect |
| 4. C113×#1381 | C2 | semidirect |
| 73. C22×C113 | #368 | semidirect |
| 80. #12837 | C113 | direct (N × H) |
| 86. C2×#368 | C2×C113 | semidirect |
| 88. #1381 | C2×C113 | semidirect |
| 89. C113 | #12837 | direct (N × H) |
| 158. C22 | #368×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C16×C113 | 2 |
| C2×#368×C113 | 2 |
| C113×#1810 | 2 |
| C113×#1381 | 2 |
| #12837 | 113 |