Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
292 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 292 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, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | C4×D4×C37 | C2 |
| hypercenter | C4×D4 | D37 |
| hypocenter | C37 | #547 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10596964 | C2 | semidirect |
| 2. #11924536 | C2 | semidirect |
| 3. #11924520 | C2 | semidirect |
| 4. #11924516 | C2 | semidirect |
| 5. #11924510 | C2 | semidirect |
| 6. C4×D148 | C2 | semidirect |
| 7. C2×C4⋊Dic37 | C2 | semidirect |
| 8. C4×D4×C37 | C2 | semidirect |
| 28. D4×C37 | D4 | semidirect |
| 51. C4×C37 | #41 | semidirect |
| 60. C37 | #547 | semidirect |
| 67. C4×D4 | D37 | semidirect |
| 91. D4 | D148 | semidirect |
| 113. C4 | #10596964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596964 | 2 |
| #11924536 | 2 |
| #11924520 | 2 |
| #11924516 | 2 |
| #11924510 | 2 |
| C4×D148 | 2 |
| C2×C4⋊Dic37 | 2 |
| C4×D4×C37 | 2 |
| #547 | 37 |