Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #127×C73 | C4 |
| hypercenter | #127 | #64408 |
| hypocenter | C73 | C4×#127 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×#64408 | C2 | semidirect |
| 2. #17989539 | C2 | semidirect |
| 3. #17989533 | C2 | semidirect |
| 4. C42×#64408 | C2 | semidirect |
| 13. #14556588 | C4 | semidirect |
| 14. #14556587 | C4 | semidirect |
| 16. #127×C73 | C4 | semidirect |
| 24. C4×#64408 | D4 | semidirect |
| 26. C2×D292 | C2×C4 | semidirect |
| 27. C2×C22⋊D73 | C2×C4 | semidirect |
| 31. C4×Dic73 | C2×C4 | semidirect |
| 32. C2×D4×C73 | C2×C4 | semidirect |
| 33. C42×C73 | C2×C4 | semidirect |
| 60. #64408 | #127 | direct (N × H) |
| 61. C4×C73 | C4×D4 | semidirect |
| 62. Dic73 | C4×D4 | semidirect |
| 69. C73 | C4×#127 | semidirect |
| 79. #127 | #64408 | direct (N × H) |
| 91. C2×D4 | C2×#64408 | semidirect |
| 102. C42 | C2×#64408 | semidirect |
| 131. C4 | D4×#64408 | semidirect |