Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C103 | C2×AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C103 |
| Frattini, cosocle | C4⋊Q8 | C23×C103 |
| prime radical | C2×2−1+4×C103 | C4 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ C2×C4⋊Q8×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#356×C103 | C2 | semidirect |
| 3. C103×#1558 | C2 | semidirect |
| 4. C103×#1405 | C2 | semidirect |
| 17. #356×C103 | C22 | semidirect |
| 19. #333×C103 | C22 | semidirect |
| 162. #13573 | C103 | direct (N × H) |
| 169. C2×#356 | C2×C103 | semidirect |
| 170. #1558 | C2×C103 | semidirect |
| 171. #1405 | C2×C103 | semidirect |
| 172. C103 | #13573 | direct (N × H) |
| 185. #356 | C22×C103 | semidirect |
| 187. #333 | C22×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#456×C103 | 2 |
| C2×#356×C103 | 2 |
| C103×#1558 | 2 |
| C103×#1405 | 2 |
| #13573 | 103 |