Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C103 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C103 |
| prime radical | C103×#2619 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×#117×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#1740 | C2 | semidirect |
| 3. C103×#1458 | C2 | semidirect |
| 4. C103×#1343 | C2 | semidirect |
| 5. C2×#127×C103 | C4 | semidirect |
| 11. #394×C103 | C4 | semidirect |
| 15. #382×C103 | C4 | semidirect |
| 169. #11693 | C103 | direct (N × H) |
| 179. #1740 | C2×C103 | semidirect |
| 180. #1458 | C2×C103 | semidirect |
| 181. #1343 | C2×C103 | semidirect |
| 182. C103 | #11693 | direct (N × H) |
| 183. C2×#127 | C4×C103 | semidirect |
| 189. #394 | C4×C103 | semidirect |
| 193. #382 | C4×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2619 | 2 |
| C103×#1740 | 2 |
| C103×#1458 | 2 |
| C103×#1343 | 2 |
| #11693 | 103 |