Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | C2×D4×C113 | C4 |
| hypercenter | C2×D4 | #90673 |
| hypocenter | C113 | #435 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14268656 | C2 | semidirect |
| 2. C22×#11744753 | C2 | semidirect |
| 3. #16813689 | C2 | semidirect |
| 4. C22⋊#11744753 | C2 | semidirect |
| 5. C22⋊#11744753 | C2 | semidirect |
| 6. #16813677 | C2 | semidirect |
| 36. #11744753 | D4 | semidirect |
| 42. C22×C113 | M16 | semidirect |
| 55. C113 | #435 | semidirect |
| 98. C22 | #14268656 | semidirect |