Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#64408 |
| commutator, socle | C2×C73 | C24×C4 |
| Fitting | 2−1+4×C73 | C4 |
| hypercenter | 2−1+4 | #64408 |
| hypocenter | C73 | C4×2−1+4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989656 | C2 | semidirect |
| 2. #17989655 | C2 | semidirect |
| 3. #41×#64408 | C2 | semidirect |
| 4. C2×Q8×#64408 | C2 | semidirect |
| 14. #14556639 | C4 | semidirect |
| 15. #14556638 | C4 | semidirect |
| 18. 2−1+4×C73 | C4 | semidirect |
| 26. #11924029 | C2×C4 | semidirect |
| 27. #11924028 | C2×C4 | semidirect |
| 28. #11924027 | C2×C4 | semidirect |
| 29. C2×Dic146 | C2×C4 | semidirect |
| 30. Q8×D73 | C2×C4 | semidirect |
| 34. #41×C73 | C2×C4 | semidirect |
| 35. C2×Q8×C73 | C2×C4 | semidirect |
| 58. #64408 | 2−1+4 | direct (N × H) |
| 67. C73 | C4×2−1+4 | semidirect |
| 75. 2−1+4 | #64408 | direct (N × H) |
| 89. #41 | C2×#64408 | semidirect |
| 93. C2×Q8 | C2×#64408 | semidirect |