Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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, socle | C22×C73 | C23×C4 |
| Fitting | #127×C73 | C4 |
| hypercenter | #127 | #64408 |
| hypocenter | C73 | #2931 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556678 | C2 | semidirect |
| 2. #17989622 | C2 | semidirect |
| 3. D4×#10596833 | C2 | semidirect |
| 4. #17989591 | C2 | semidirect |
| 5. #17989561 | C2 | semidirect |
| 6. C4×#11924036 | C2 | semidirect |
| 28. #11924036 | D4 | semidirect |
| 74. C4×C73 | #131 | semidirect |
| 84. C73 | #2931 | semidirect |
| 162. C4 | #14556678 | semidirect |