Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
592 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #391×C83 | C2 |
| hypercenter | #391 | D83 |
| hypocenter | C83 | #2733 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581781 | C2 | semidirect |
| 2. #19127618 | C2 | semidirect |
| 3. #19127611 | C2 | semidirect |
| 4. #19127603 | C2 | semidirect |
| 5. #19127593 | C2 | semidirect |
| 6. #391×C83 | C2 | semidirect |
| 40. C2×Q8×C83 | D4 | semidirect |
| 97. C83 | #2733 | semidirect |
| 101. #391 | D83 | semidirect |
| 122. C2×Q8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581781 | 2 |
| #19127618 | 2 |
| #19127611 | 2 |
| #19127603 | 2 |
| #19127593 | 2 |
| #391×C83 | 2 |
| #2733 | 83 |