Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
802 conjugacy classes of subgroups; only the 334 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 334 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C113 | C23 |
| commutator | C23 | C2×C42×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle | C23×C113 | C2×C42 |
| prime radical | C24×C113 | C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C113×#1273 | C2 | semidirect |
| 27. C2×C8×C113 | M16 | semidirect |
| 50. #7852 | C113 | direct (N × H) |
| 55. #1273 | C2×C113 | semidirect |
| 56. C113 | #7852 | direct (N × H) |
| 81. C2×C8 | M16×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×M16×C113 | 2 |
| C113×#1273 | 2 |
| #7852 | 113 |