Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
272 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4 | C22×D73 |
| commutator | C22×C73 | C2×C42 |
| Fitting | #336×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | #336 | D73 |
| hypocenter | C73 | #1771 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #14556520 | C4 | semidirect |
| 15. #14556501 | C4 | semidirect |
| 65. #10596831 | C4⋊C4 | semidirect |
| 85. C73 | #1771 | semidirect |