Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 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×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | C4×#41×C83 | C2 |
| prime radical | C2×#41×C83 | C22 |
| hypercenter | C4×#41 | D83 |
| hypocenter | C83 | #3504 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128427 | C2 | semidirect |
| 2. #19128410 | C2 | semidirect |
| 3. #19128329 | C2 | semidirect |
| 4. #19128258 | C2 | semidirect |
| 5. C2×#14581784 | C2 | semidirect |
| 39. #41×C83 | Q8 | semidirect |
| 75. C83 | #3504 | semidirect |
| 103. #41 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128427 | 2 |
| #19128410 | 2 |
| #19128329 | 2 |
| #19128258 | 2 |
| C2×#14581784 | 2 |
| #19128184 | 2 |
| C4×#41×C83 | 2 |
| #3504 | 83 |