Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17988463 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #410×C73 | C2 |
| socle | C2×C73 | #386 |
| hypercenter | #410 | D73 |
| hypocenter | C73 | #1904 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #410 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989061 | C2 | semidirect |
| 3. #17988604 | C2 | semidirect |
| 4. #17988591 | C2 | semidirect |
| 5. #17988357 | C2 | semidirect |
| 6. #17988343 | C2 | semidirect |
| 7. #410×C73 | C2 | semidirect |
| 11. C2×#11924015 | C4 | semidirect |
| 12. C2×#11924013 | C4 | semidirect |
| 40. C2×#10596831 | C2×C4 | semidirect |
| 49. C2×Q8×C73 | C2×C4 | semidirect |
| 51. C2×D4×C73 | C2×C4 | semidirect |
| 116. C73 | #1904 | semidirect |
| 121. #410 | D73 | semidirect |
| 146. C2×Q8 | C4×D73 | semidirect |
| 154. C2×D4 | C4×D73 | semidirect |