Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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 | C2×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C23×C4 | #64408 |
| hypocenter | C73 | C23×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11924038 | C2 | semidirect |
| 2. C2×D73⋊M16 | C2 | direct (N × H) |
| 3. C22×#11924037 | C2 | semidirect |
| 4. C22×#11924036 | C2 | semidirect |
| 6. C2×#11924038 | C22 | semidirect |
| 7. D73⋊M16 | C22 | direct (N × H) |
| 8. C2×#11924037 | C22 | semidirect |
| 9. C2×#11924036 | C22 | semidirect |
| 10. C22×#10596833 | C22 | semidirect |
| 20. #11924038 | C23 | semidirect |
| 21. #11924037 | C23 | semidirect |
| 22. #11924036 | C23 | semidirect |
| 23. C2×#10596833 | C23 | semidirect |
| 49. C22×D73 | M16 | semidirect |
| 67. #10596833 | C24 | semidirect |
| 69. C22×C73 | C2×M16 | semidirect |
| 74. C2×D73 | C2×M16 | semidirect |
| 83. C2×C73 | C22×M16 | semidirect |
| 86. D73 | C22×M16 | semidirect |
| 88. C73 | C23×M16 | semidirect |
| 162. C22 | D73⋊M16 | direct (N × H) |
| 173. C2 | C2×D73⋊M16 | direct (N × H) |