Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #393×C83 | C2 |
| hypercenter | #393 | D83 |
| hypocenter | C83 | #2615 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13050591 | C2 | semidirect |
| 2. C2×#14581765 | C2 | semidirect |
| 3. #19127612 | C2 | semidirect |
| 4. #19127611 | C2 | semidirect |
| 5. #19127610 | C2 | semidirect |
| 6. #19127560 | C2 | semidirect |
| 7. #393×C83 | C2 | semidirect |
| 35. C2×C4×D83 | D4 | semidirect |
| 94. C83 | #2615 | semidirect |
| 98. #393 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050591 | 2 |
| C2×#14581765 | 2 |
| #19127612 | 2 |
| #19127611 | 2 |
| #19127610 | 2 |
| #19127560 | 2 |
| #393×C83 | 2 |
| #2615 | 83 |