Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D73 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C42 | C22×D73 |
| Fitting | #335×C73 | C2 |
| socle | C22×C73 | C4×D4 |
| hypercenter | #335 | D73 |
| hypocenter | C73 | #1581 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #335 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988664 | C2 | semidirect |
| 3. #17988652 | C2 | semidirect |
| 4. #17988314 | C2 | semidirect |
| 5. #17988314 | C2 | semidirect |
| 6. #17988309 | C2 | semidirect |
| 7. #335×C73 | C2 | semidirect |
| 52. D292 | M16 | semidirect |
| 63. #10596831 | D8 | semidirect |
| 84. C73 | #1581 | semidirect |
| 88. #335 | D73 | semidirect |