Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
398 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C103 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C103 |
| Frattini, cosocle | C22×C8 | C23×C103 |
| socle | C22×C103 | C2×C22⋊C8 |
| prime radical | #525×C103 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C103 ◁ C23×C8×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C16×C103 | C2 | semidirect |
| 3. C103×#1323 | C2 | semidirect |
| 4. C103×#1315 | C2 | semidirect |
| 118. #11468 | C103 | direct (N × H) |
| 125. C2×C22⋊C16 | C2×C103 | semidirect |
| 126. #1323 | C2×C103 | semidirect |
| 127. #1315 | C2×C103 | semidirect |
| 128. C103 | #11468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2929 | 2 |
| C2×C22⋊C16×C103 | 2 |
| C103×#1323 | 2 |
| C103×#1315 | 2 |
| #11468 | 103 |