Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
2550 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C103 | C24 |
| commutator | C22 | C24×C4×C103 |
| Frattini, cosocle | C23 | C25×C103 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#2356 | C2 | direct (N × H) |
| 11. C2×C4×Q8×C103 | C4 | semidirect |
| 47. C4×Q8×C103 | C2×C4 | semidirect |
| 167. C2×#2356 | C103 | direct (N × H) |
| 168. C2×C103 | #2356 | direct (N × H) |
| 175. #2356 | C2×C103 | direct (N × H) |
| 183. C103 | C2×#2356 | direct (N × H) |
| 185. C2×C4×Q8 | C4×C103 | semidirect |
| 221. C4×Q8 | C2×C4×C103 | semidirect |
| 341. C2 | C103×#2356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Q8×C103 | 2 |
| C103×#2356 | 2 |
| C2×#391×C103 | 2 |
| C2×#387×C103 | 2 |
| C2×#383×C103 | 2 |
| C2×#382×C103 | 2 |
| C2×C4×C4⋊C4×C103 | 2 |
| C2×#376×C103 | 2 |
| C2×#2356 | 103 |