Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
208 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C83 | C23 |
| commutator | C22 | C2×C42×C83 |
| Frattini, cosocle | C42 | C23×C83 |
| socle | C22×C83 | C2×C42 |
| prime radical | C23×C83 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #322×C83 | C2 | semidirect |
| 5. #322×C83 | C2 | semidirect |
| 43. C8×C83 | M16 | semidirect |
| 58. #1451 | C83 | direct (N × H) |
| 59. C83 | #1451 | direct (N × H) |
| 63. #322 | C2×C83 | semidirect |
| 64. #322 | C2×C83 | semidirect |
| 102. C8 | M16×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #431×C83 | 2 |
| C4×M16×C83 | 2 |
| C2×C4×C8×C83 | 2 |
| #322×C83 | 2 |
| #1451 | 83 |