Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C23×D113 |
| commutator, socle | C22×C113 | C24 |
| Fitting | C22×Q8×C113 | C2 |
| hypercenter | C22×Q8 | D113 |
| hypocenter | C113 | D4×Q8 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D113 | C2 | semidirect |
| 2. #16813620 | C2 | semidirect |
| 3. #16813601 | C2 | semidirect |
| 4. #16813598 | C2 | semidirect |
| 5. Q8×Dic113 | C2 | semidirect |
| 7. C22×Q8×C113 | C2 | semidirect |
| 25. Q8×C113 | D4 | semidirect |
| 29. C22⋊D113 | Q8 | direct (N × H) |
| 37. C22×C113 | C2×Q8 | semidirect |
| 41. C2×D113 | C2×Q8 | semidirect |
| 46. Dic113 | C2×Q8 | semidirect |
| 52. C113 | D4×Q8 | semidirect |
| 55. C22×Q8 | D113 | semidirect |
| 79. Q8 | C22⋊D113 | direct (N × H) |
| 93. C22 | Q8×D113 | semidirect |