Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C22×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Frattini | C22 | C23×D37 |
| Fitting | #117×C37 | C2 |
| hypercenter | #117 | D37 |
| hypocenter | C37 | #525 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10596962 | C2 | semidirect |
| 2. C22×C4×D37 | C2 | semidirect |
| 3. #11924520 | C2 | semidirect |
| 4. #11924516 | C2 | semidirect |
| 5. #11924511 | C2 | semidirect |
| 6. #11924506 | C2 | semidirect |
| 7. C4×D148 | C2 | semidirect |
| 8. #117×C37 | C2 | semidirect |
| 15. C2×D148 | C22 | semidirect |
| 19. C2×C4×D37 | C22 | semidirect |
| 20. C2×Dic74 | C22 | semidirect |
| 21. C4⋊C4×C37 | C22 | semidirect |
| 23. C42×C37 | C22 | semidirect |
| 25. #10596938 | C22 | semidirect |
| 26. C4⋊Dic37 | C22 | semidirect |
| 32. C2×C4×C37 | D4 | semidirect |
| 54. C2×D37 | #41 | semidirect |
| 66. C37 | #525 | semidirect |
| 74. #117 | D37 | semidirect |
| 88. C4⋊C4 | C2×D37 | semidirect |
| 92. C42 | C2×D37 | semidirect |
| 108. C2×C4 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| C22×C4×D37 | 2 |
| #11924520 | 2 |
| #11924516 | 2 |
| #11924511 | 2 |
| #11924506 | 2 |
| C4×D148 | 2 |
| #117×C37 | 2 |
| #525 | 37 |