Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
638 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3330 | C2 | semidirect |
| 2. C41×#1710 | C2 | semidirect |
| 3. C41×#1699 | C2 | semidirect |
| 4. C41×#1647 | C2 | semidirect |
| 5. C41×#1589 | C2 | semidirect |
| 81. #20304 | C41 | direct (N × H) |
| 91. #3330 | C2×C41 | semidirect |
| 92. #1710 | C2×C41 | semidirect |
| 93. #1699 | C2×C41 | semidirect |
| 94. #1647 | C2×C41 | semidirect |
| 95. #1589 | C2×C41 | semidirect |
| 114. C41 | #20304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3330 | 2 |
| C41×#1710 | 2 |
| C41×#1699 | 2 |
| C41×#1647 | 2 |
| C41×#1589 | 2 |
| #20304 | 41 |