Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C24×D293 |
| commutator, socle, cosocle | C22×C293 | C25 |
| Fitting | C23×Q8×C293 | C2 |
| hypercenter | C23×Q8 | D293 |
| hypocenter | C293 | #3486 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22627672 | C2 | semidirect |
| 2. Q8×C22⋊D293 | C2 | semidirect |
| 3. #34036790 | C2 | semidirect |
| 4. #34036703 | C2 | semidirect |
| 5. #34036640 | C2 | semidirect |
| 6. #34036607 | C2 | semidirect |
| 7. C23×Q8×C293 | C2 | semidirect |
| 9. C2×#17989803 | C22 | semidirect |
| 11. C2×Q8×D293 | C22 | semidirect |
| 12. #22627622 | C22 | semidirect |
| 13. #22627613 | C22 | semidirect |
| 16. #22627600 | C22 | semidirect |
| 19. Q8×Dic293 | C22 | semidirect |
| 44. C2×Q8×C293 | D4 | semidirect |
| 75. C22×C293 | 2−1+4 | semidirect |
| 88. C293 | #3486 | semidirect |
| 91. C23×Q8 | D293 | semidirect |
| 123. C2×Q8 | C22⋊D293 | semidirect |
| 166. C22 | #22627672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627672 | 2 |
| Q8×C22⋊D293 | 2 |
| #34036790 | 2 |
| #34036703 | 2 |
| #34036640 | 2 |
| #34036607 | 2 |
| C23×Q8×C293 | 2 |
| #3486 | 293 |