Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | C22×M16×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C22×M16 | D73 |
| hypocenter | C73 | C2×#407 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11924012 | C2 | semidirect |
| 3. #17988550 | C2 | direct (N × H) |
| 4. C2×#14556503 | C2 | semidirect |
| 5. C22×M16×C73 | C2 | semidirect |
| 15. C2×#11924012 | C22 | semidirect |
| 16. C22×#10596831 | C22 | semidirect |
| 17. #14556503 | C22 | semidirect |
| 20. C2×M16×C73 | C22 | semidirect |
| 21. C22×C8×C73 | C22 | semidirect |
| 40. C2×#10596831 | C23 | semidirect |
| 50. C2×C8×C73 | C23 | semidirect |
| 60. C22×D73 | M16 | semidirect |
| 90. C2×D73 | C2×M16 | semidirect |
| 97. C2×C73 | #407 | semidirect |
| 102. C73 | C2×#407 | semidirect |
| 105. C22×M16 | D73 | semidirect |
| 120. C2×M16 | C2×D73 | semidirect |
| 122. C22×C8 | C2×D73 | semidirect |
| 152. C2×C8 | C22×D73 | semidirect |
| 200. C2 | #17988550 | direct (N × H) |