Order 3328.
1934 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D13 |
| commutator, socle, prime radical, cosocle | C24×C13 | C24 |
| Fitting | C4×C13×#95 | C2 |
| hypercenter | C4×#95 | D13 |
| hypocenter | C13 | #15143 |
| LCS | G ▷ C24×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 41. C2×C42×C13 | Q8 | semidirect |
| 54. C2×C4⋊Dic13 | Q8 | semidirect |
| 59. C13×#95 | Q8 | semidirect |
| 145. C2×C4×C13 | C4⋊Q8 | semidirect |
| 199. C4×C13 | #395 | semidirect |
| 233. C2×C42 | Dic26 | semidirect |
| 237. #95 | Dic26 | semidirect |
| 295. C13 | #15143 | semidirect |
| 334. C2×C4 | #88123 | semidirect |
| 363. C4 | #11718317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88123 | 2 |
| C2×#11718317 | 2 |
| C2×#11718589 | 2 |
| C2×#11718596 | 2 |
| #13113101 | 2 |
| #13113066 | 2 |
| C4×C13×#95 | 2 |
| #15143 | 13 |