Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
2882 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 2882 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C103 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C103 |
| prime radical | C26×C103 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#393×C103 | C2 | semidirect |
| 3. C103×#1440 | C2 | semidirect |
| 4. C103×#1437 | C2 | semidirect |
| 6. C23×Q8×C103 | C22 | semidirect |
| 11. C22×C42×C103 | C22 | semidirect |
| 14. C2×#95×C103 | C22 | semidirect |
| 15. C2×#95×C103 | C22 | semidirect |
| 16. C2×#95×C103 | C22 | semidirect |
| 17. C2×#95×C103 | C22 | semidirect |
| 164. #15467 | C103 | direct (N × H) |
| 171. C2×#393 | C2×C103 | semidirect |
| 173. #1440 | C2×C103 | semidirect |
| 174. #1437 | C2×C103 | semidirect |
| 175. C103 | #15467 | direct (N × H) |
| 177. C23×Q8 | C22×C103 | semidirect |
| 182. C22×C42 | C22×C103 | semidirect |
| 185. C2×#95 | C22×C103 | semidirect |
| 186. C2×#95 | C22×C103 | semidirect |
| 187. C2×#95 | C22×C103 | semidirect |
| 188. C2×#95 | C22×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#393×C103 | 2 |
| C2×#379×C103 | 2 |
| C103×#1440 | 2 |
| C103×#1437 | 2 |
| #15467 | 103 |