Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
804 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #385×C73 | C2 |
| hypercenter | #385 | D73 |
| hypocenter | C73 | #2675 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556566 | C2 | semidirect |
| 2. C2×#14556565 | C2 | semidirect |
| 3. C2×#14556564 | C2 | semidirect |
| 4. #17988509 | C2 | semidirect |
| 5. #17988497 | C2 | semidirect |
| 6. #17988496 | C2 | semidirect |
| 7. #17988496 | C2 | semidirect |
| 8. #17988461 | C2 | semidirect |
| 9. #385×C73 | C2 | semidirect |
| 63. #11924005 | D4 | semidirect |
| 73. C22⋊C4×C73 | D4 | semidirect |
| 157. C73 | #2675 | semidirect |
| 166. #385 | D73 | semidirect |
| 230. C22⋊C4 | D292 | semidirect |