Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #391×C73 | C2 |
| hypercenter | #391 | D73 |
| hypocenter | C73 | #2431 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11924029 | C2 | semidirect |
| 2. C2×#14556588 | C2 | semidirect |
| 3. C2×#14556580 | C2 | semidirect |
| 4. C2×#14556566 | C2 | semidirect |
| 5. #17988497 | C2 | semidirect |
| 6. #17988488 | C2 | semidirect |
| 7. #17988465 | C2 | semidirect |
| 8. C4×#11924005 | C2 | semidirect |
| 9. #391×C73 | C2 | semidirect |
| 50. C2×D292 | D4 | semidirect |
| 58. C2×C4×D73 | D4 | semidirect |
| 66. C2×Q8×C73 | D4 | semidirect |
| 100. C2×C4×C73 | #41 | semidirect |
| 149. C73 | #2431 | semidirect |
| 155. #391 | D73 | semidirect |
| 188. C2×Q8 | D292 | semidirect |
| 262. C2×C4 | #11924029 | semidirect |