Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D37 |
| commutator, cosocle | C22×C37 | C24 |
| Frattini | C22 | C23×D37 |
| Fitting | C2×C4⋊C4×C37 | C2 |
| socle | C23×C37 | C23 |
| hypercenter | C2×C4⋊C4 | D37 |
| hypocenter | C37 | C2×#121 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D148 | C2 | semidirect |
| 2. C22×D148 | C2 | semidirect |
| 3. C22×C4×D37 | C2 | semidirect |
| 4. #11924511 | C2 | direct (N × H) |
| 5. C2×#10596938 | C2 | semidirect |
| 6. C2×C4⋊C4×C37 | C2 | semidirect |
| 14. C2×D148 | C22 | semidirect |
| 15. C2×D148 | C22 | semidirect |
| 17. C2×C4×D37 | C22 | semidirect |
| 18. C4⋊C4×C37 | C22 | semidirect |
| 19. #10596938 | C22 | semidirect |
| 26. C22×D37 | D4 | semidirect |
| 30. C2×C4×C37 | D4 | semidirect |
| 49. C2×D37 | C2×D4 | semidirect |
| 51. C4×C37 | C2×D4 | semidirect |
| 53. C2×C37 | #121 | semidirect |
| 60. C37 | C2×#121 | semidirect |
| 65. C2×C4⋊C4 | D37 | semidirect |
| 78. C4⋊C4 | C2×D37 | semidirect |
| 95. C2×C4 | D148 | semidirect |
| 112. C4 | C2×D148 | semidirect |
| 115. C2 | #11924511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D148 | 2 |
| C22×C4×D37 | 2 |
| #11924511 | 2 |
| C2×#10596938 | 2 |
| C2×C4⋊C4×C37 | 2 |
| C2×#121 | 37 |