Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D113 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | C2×M16×C113 | C2 |
| hypercenter | C2×M16 | D113 |
| hypocenter | C113 | #435 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C8×D113 | C2 | semidirect |
| 3. #16813551 | C2 | semidirect |
| 4. C22⋊#11744751 | C2 | semidirect |
| 5. #16813534 | C2 | semidirect |
| 6. #16813532 | C2 | semidirect |
| 7. C2×M16×C113 | C2 | semidirect |
| 34. C8×C113 | D4 | semidirect |
| 43. C2×D113 | M16 | semidirect |
| 55. C113 | #435 | semidirect |
| 57. C2×M16 | D113 | semidirect |
| 92. C8 | C22⋊D113 | semidirect |