Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
510 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 94 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×C103 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C103 |
| Frattini, cosocle | #124 | C23×C103 |
| prime radical | C2×#454×C103 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ C2×#124×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#354×C103 | C2 | semidirect |
| 3. C2×#329×C103 | C2 | semidirect |
| 4. C103×#1404 | C2 | direct (N × H) |
| 5. C2×2−1+4×C103 | C4 | semidirect |
| 10. #454×C103 | C4 | semidirect |
| 13. C2×#101×C103 | C4 | semidirect |
| 17. #354×C103 | C22 | semidirect |
| 19. #329×C103 | C22 | semidirect |
| 23. 2−1+4×C103 | C2×C4 | semidirect |
| 48. #101×C103 | C2×C4 | semidirect |
| 170. C2×#1404 | C103 | direct (N × H) |
| 176. C2×C103 | #1404 | direct (N × H) |
| 179. C2×#354 | C2×C103 | semidirect |
| 180. C2×#329 | C2×C103 | semidirect |
| 181. #1404 | C2×C103 | direct (N × H) |
| 182. C103 | C2×#1404 | direct (N × H) |
| 183. C2×2−1+4 | C4×C103 | semidirect |
| 188. #454 | C4×C103 | semidirect |
| 191. C2×#101 | C4×C103 | semidirect |
| 195. #354 | C22×C103 | semidirect |
| 197. #329 | C22×C103 | semidirect |
| 201. 2−1+4 | C2×C4×C103 | semidirect |
| 226. #101 | C2×C4×C103 | semidirect |
| 353. C2 | C103×#1404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#454×C103 | 2 |
| C2×#354×C103 | 2 |
| C2×#329×C103 | 2 |
| C103×#1404 | 2 |
| C2×#1404 | 103 |