Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
292 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 91 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×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C2×Q8×C73 | C8 |
| hypercenter | C2×Q8 | #10596842 |
| hypocenter | C73 | #1984 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. C2×#10596842 | Q8 | semidirect |
| 30. C2×Dic146 | C8 | semidirect |
| 31. C2×Dic146 | C8 | semidirect |
| 36. C2×Q8×C73 | C8 | semidirect |
| 79. C73 | #1984 | semidirect |
| 99. C2×Q8 | #10596842 | semidirect |