Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D292 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C42 | C22×D73 |
| Fitting | C82×C73 | C2 |
| socle | C22×C73 | C4×D4 |
| hypercenter | C82 | D73 |
| hypocenter | C73 | #1590 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 ◁ C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17988717 | C2 | semidirect |
| 4. #17988338 | C2 | semidirect |
| 5. #17988319 | C2 | semidirect |
| 7. C82×C73 | C2 | semidirect |
| 57. C8×C73 | M16 | semidirect |
| 58. C8×C73 | SD16 | semidirect |
| 78. C73 | #1590 | semidirect |
| 85. C82 | D73 | semidirect |
| 137. C8 | #11924011 | semidirect |
| 138. C8 | #11924017 | semidirect |