Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 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 | 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. C22×Dic74 | C2 | semidirect |
| 2. C2×Q8×D37 | C2 | semidirect |
| 3. #11924535 | C2 | semidirect |
| 4. #11924534 | C2 | semidirect |
| 5. #11924516 | C2 | semidirect |
| 6. #11924514 | C2 | semidirect |
| 7. #11924513 | C2 | semidirect |
| 8. #11924501 | C2 | semidirect |
| 11. C22⋊Q8×C37 | C2 | semidirect |
| 45. C22⋊D37 | Q8 | semidirect |
| 57. Dic74 | D4 | semidirect |
| 60. C22×C37 | C2×Q8 | semidirect |
| 64. C2×D37 | C2×Q8 | semidirect |
| 73. Dic37 | C2×Q8 | semidirect |
| 80. C37 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D37 | semidirect |
| 143. C22 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic74 | 2 |
| C2×Q8×D37 | 2 |
| #11924535 | 2 |
| #11924534 | 2 |
| #11924516 | 2 |
| #11924514 | 2 |
| #11924513 | 2 |
| #11924501 | 2 |
| C4×C22⋊D37 | 2 |
| #11924496 | 2 |
| C22⋊Q8×C37 | 2 |
| D4×Q8 | 37 |