Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C53 | #99 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C53 |
| socle | C22×C53 | C2×#99 |
| prime radical | C22×#41×C53 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C53 ◁ C22×C4×C53 ◁ C2×#117×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1458 | C2 | semidirect |
| 3. C53×#1319 | C2 | semidirect |
| 4. C53×#1318 | C2 | semidirect |
| 21. C2×#41×C53 | C8 | semidirect |
| 137. #11431 | C53 | direct (N × H) |
| 163. #1458 | C2×C53 | semidirect |
| 164. #1319 | C2×C53 | semidirect |
| 165. #1318 | C2×C53 | semidirect |
| 185. C53 | #11431 | direct (N × H) |
| 190. C2×#41 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2297 | 2 |
| C53×#1458 | 2 |
| C53×#1319 | 2 |
| C53×#1318 | 2 |
| #11431 | 53 |