Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
454 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C23×C103 | #121 |
| 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 |
|---|---|---|
| 164. #10119 | C103 | direct (N × H) |
| 176. C103 | #10119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#3255 | 2 |
| C103×#3229 | 2 |
| C103×#3165 | 2 |
| C103×#1997 | 2 |
| C103×#1526 | 2 |
| C103×#1485 | 2 |
| C103×#1299 | 2 |
| #10119 | 103 |