Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
256 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D73 |
| commutator | C22×C4×C73 | C23 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #340×C73 | C2 |
| socle | C23×C73 | C2×D4 |
| hypercenter | #340 | D73 |
| hypocenter | C73 | #2075 |
| LCS | G ▷ C22×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556524 | C2 | semidirect |
| 5. #17988350 | C2 | semidirect |
| 6. #17988349 | C2 | semidirect |
| 7. #340×C73 | C2 | semidirect |
| 117. C73 | #2075 | semidirect |
| 124. #340 | D73 | semidirect |