Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C2×#126×C73 | C2 |
| hypercenter | C2×#126 | D73 |
| hypocenter | C73 | #2852 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C42×D73 | C2 | semidirect |
| 2. #17988475 | C2 | semidirect |
| 3. #17988468 | C2 | semidirect |
| 5. #17988458 | C2 | semidirect |
| 6. #17988455 | C2 | semidirect |
| 7. C2×#126×C73 | C2 | semidirect |
| 40. C42×C73 | D4 | semidirect |
| 71. C2×D73 | #126 | semidirect |
| 83. C73 | #2852 | semidirect |
| 84. C2×#126 | D73 | semidirect |
| 123. C42 | C22⋊D73 | semidirect |