Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C4×C22⋊C4×C73 | C2 |
| hypercenter | C4×C22⋊C4 | D73 |
| hypocenter | C73 | #2433 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D292 | C2 | semidirect |
| 2. C2×#14556588 | C2 | semidirect |
| 3. C2×#14556565 | C2 | semidirect |
| 4. C2×#14556561 | C2 | semidirect |
| 5. #17988497 | C2 | semidirect |
| 6. #17988489 | C2 | semidirect |
| 7. C4×C22⋊C4×C73 | C2 | semidirect |
| 13. C22×D292 | C22 | semidirect |
| 14. C22×D292 | C22 | semidirect |
| 19. C2×C4⋊Dic73 | C22 | semidirect |
| 20. C2×#11924005 | C22 | semidirect |
| 21. C2×#11924005 | C22 | semidirect |
| 24. C2×C42×C73 | C22 | semidirect |
| 25. #95×C73 | C22 | semidirect |
| 42. C2×D292 | D4 | semidirect |
| 51. C22×C4×C73 | D4 | semidirect |
| 55. C22⋊C4×C73 | D4 | semidirect |
| 82. C2×C4×C73 | C2×D4 | semidirect |
| 93. C22×C73 | #127 | semidirect |
| 110. C4×C73 | #120 | semidirect |
| 120. C73 | #2433 | semidirect |
| 127. C4×C22⋊C4 | D73 | semidirect |
| 144. C2×C42 | C2×D73 | semidirect |
| 145. #95 | C2×D73 | semidirect |
| 168. C22×C4 | D292 | semidirect |
| 175. C22⋊C4 | D292 | semidirect |
| 209. C2×C4 | C2×D292 | semidirect |
| 223. C22 | #14556588 | semidirect |
| 231. C4 | #14556561 | semidirect |