Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 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 | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C4 | C23×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C22×M32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556666 | C2 | semidirect |
| 2. #17989643 | C2 | direct (N × H) |
| 3. C2×#14556665 | C2 | semidirect |
| 4. C2×#14556664 | C2 | semidirect |
| 6. #14556666 | C22 | semidirect |
| 7. #14556665 | C22 | semidirect |
| 8. #14556664 | C22 | semidirect |
| 9. C2×#11924031 | C22 | semidirect |
| 19. #11924031 | C23 | semidirect |
| 70. C2×D73 | M32 | semidirect |
| 79. C2×C73 | C2×M32 | semidirect |
| 82. D73 | C2×M32 | semidirect |
| 84. C73 | C22×M32 | semidirect |
| 165. C2 | #17989643 | direct (N × H) |