Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D37 |
| commutator, cosocle | C4×C37 | C24 |
| Frattini | C4 | C23×D37 |
| Fitting | 2−1+4×C37 | C2 |
| socle | C2×C37 | C22×D4 |
| hypercenter | 2−1+4 | D37 |
| hypocenter | C37 | #578 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924583 | C2 | semidirect |
| 2. #11924567 | C2 | semidirect |
| 3. #11924566 | C2 | semidirect |
| 4. #11924556 | C2 | semidirect |
| 5. C2×#10596942 | C2 | semidirect |
| 6. #11924543 | C2 | semidirect |
| 7. 2−1+4×C37 | C2 | semidirect |
| 53. C37 | #578 | semidirect |
| 55. 2−1+4 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924583 | 2 |
| #11924567 | 2 |
| #11924566 | 2 |
| #11924556 | 2 |
| C2×#10596942 | 2 |
| #11924543 | 2 |
| 2−1+4×C37 | 2 |
| #578 | 37 |