Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
478 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C103 |
| prime radical | #532×C103 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C103×#3104 | C2 | semidirect |
| 4. C103×#1537 | C2 | semidirect |
| 6. C103×#1467 | C2 | semidirect |
| 7. C103×#1287 | C2 | semidirect |
| 183. #10041 | C103 | direct (N × H) |
| 191. #3104 | C2×C103 | semidirect |
| 192. #1537 | C2×C103 | semidirect |
| 194. #1467 | C2×C103 | semidirect |
| 195. #1287 | C2×C103 | semidirect |
| 196. C103 | #10041 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#3216 | 2 |
| C103×#3112 | 2 |
| C103×#3104 | 2 |
| C103×#1537 | 2 |
| C103×#1496 | 2 |
| C103×#1467 | 2 |
| C103×#1287 | 2 |
| #10041 | 103 |