Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C22×Q8×C37 | C2 |
| prime radical | C2×C22⋊D37 | C22 |
| hypercenter | C22×Q8 | D37 |
| hypocenter | C37 | D4×Q8 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D37 | C2 | semidirect |
| 2. #11924534 | C2 | semidirect |
| 3. #11924515 | C2 | semidirect |
| 4. #11924512 | C2 | semidirect |
| 5. Q8×Dic37 | C2 | semidirect |
| 7. C22×Q8×C37 | C2 | semidirect |
| 25. Q8×C37 | D4 | semidirect |
| 29. C22⋊D37 | Q8 | direct (N × H) |
| 37. C22×C37 | C2×Q8 | semidirect |
| 41. C2×D37 | C2×Q8 | semidirect |
| 46. Dic37 | C2×Q8 | semidirect |
| 53. C37 | D4×Q8 | semidirect |
| 55. C22×Q8 | D37 | semidirect |
| 79. Q8 | C22⋊D37 | direct (N × H) |
| 93. C22 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D37 | 2 |
| #11924534 | 2 |
| #11924515 | 2 |
| #11924512 | 2 |
| Q8×Dic37 | 2 |
| C4×C22⋊D37 | 2 |
| C22×Q8×C37 | 2 |
| D4×Q8 | 37 |