Order 512.
2422 conjugacy classes of subgroups.
The subgroup lattice has 431 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, cosocle | C24 | C25 |
| commutator | C23 | C24×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #2582 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2582 | 2 |
| C2×#2295 | 2 |
| #14634 | 2 |
| #14314 | 2 |
| #14266 | 2 |
| #14261 | 2 |
| #14151 | 2 |
| #14046 | 2 |
| #14021 | 2 |
| #13926 | 2 |
| C4×#384 | 2 |