Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C2×#117×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C2×#117 | D73 |
| hypocenter | C73 | #2285 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17988456 | C2 | semidirect |
| 4. #17988452 | C2 | semidirect |
| 6. C4×#11924007 | C2 | semidirect |
| 13. C2×C4×Dic73 | C4 | semidirect |
| 53. C2×C4×C73 | C4⋊C4 | semidirect |
| 80. Dic73 | #117 | semidirect |
| 87. C73 | #2285 | semidirect |
| 147. C2×C4 | #11924007 | semidirect |