Finite Group DatabasebetaFinite Group DatabasebetaOrder 37952.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 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×D593 |
| commutator, socle, cosocle | C22×C593 | C24 |
| Fitting | C4×D4×C593 | C2 |
| hypercenter | C4×D4 | D593 |
| hypocenter | C593 | #540 |
| LCS | G ▷ C22×C593 ▷ C593 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #34039281 | C2 | semidirect |
| 2. #34039276 | C2 | semidirect |
| 3. #34039268 | C2 | semidirect |
| 4. #34039267 | C2 | semidirect |
| 5. #34039260 | C2 | semidirect |
| 6. #34039259 | C2 | semidirect |
| 7. #34039258 | C2 | semidirect |
| 8. #34039256 | C2 | semidirect |
| 9. C4×D2372 | C2 | semidirect |
| 10. #34039242 | C2 | semidirect |
| 11. C4×D4×C593 | C2 | semidirect |
| 79. C593 | #540 | semidirect |
| 90. C4×D4 | D593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34039281 | 2 |
| #34039276 | 2 |
| #34039268 | 2 |
| #34039267 | 2 |
| #34039260 | 2 |
| #34039259 | 2 |
| #34039258 | 2 |
| #34039256 | 2 |
| C4×D2372 | 2 |
| #34039242 | 2 |
| C4×D4×C593 | 2 |
| #540 | 593 |