Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
488 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#64408 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C22 | C23×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C42 | #64408 |
| hypocenter | C73 | C2×#432 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989610 | C2 | direct (N × H) |
| 2. C2×#14556658 | C2 | semidirect |
| 4. C2×#14556646 | C2 | semidirect |
| 7. #14556658 | C22 | semidirect |
| 9. #14556646 | C22 | semidirect |
| 79. C2×C73 | #432 | semidirect |
| 85. C73 | C2×#432 | semidirect |
| 165. C2 | #17989610 | direct (N × H) |