Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D73 |
| commutator | C22×C73 | C2×C42 |
| Fitting | #336×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | #336 | D73 |
| hypocenter | C73 | #1753 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14556502 | C2 | semidirect |
| 4. C2×C8×Dic73 | C2 | semidirect |
| 6. #17988341 | C2 | semidirect |
| 7. #336×C73 | C2 | semidirect |
| 11. C2×#11924011 | C4 | semidirect |
| 16. #14556503 | C4 | semidirect |
| 72. C2×Dic73 | M16 | semidirect |
| 80. #10596831 | C22⋊C4 | semidirect |
| 105. C73 | #1753 | semidirect |
| 112. #336 | D73 | semidirect |