Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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 | C23×#64408 |
| commutator | C2×C73 | C23×C8 |
| Fitting | C2×C22⋊C4×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C2×C22⋊C4 | #64408 |
| hypocenter | C73 | #2972 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989614 | C2 | semidirect |
| 2. #17989604 | C2 | semidirect |
| 3. #17989555 | C2 | semidirect |
| 4. C2×C22⋊#10596833 | C2 | semidirect |
| 6. C2×#11924036 | C22 | semidirect |
| 7. C22×#10596833 | C22 | semidirect |
| 8. #14556658 | C22 | semidirect |
| 9. #14556648 | C22 | semidirect |
| 11. C22⋊#10596833 | C22 | semidirect |
| 12. C4×#10596833 | C22 | semidirect |
| 26. C2×C22⋊D73 | C8 | semidirect |
| 47. C23×C73 | C2×C8 | semidirect |
| 52. C22×D73 | C2×C8 | semidirect |
| 58. C22⋊D73 | C2×C8 | semidirect |
| 63. C2×Dic73 | C2×C8 | semidirect |
| 96. C73 | #2972 | semidirect |
| 147. C23 | #11924036 | semidirect |