Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 102 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×C53 | C2×#99 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C53 |
| prime radical | C53×#392 | C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×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×#1742 | C2 | semidirect |
| 3. C53×#1464 | C2 | semidirect |
| 4. C53×#1354 | C2 | semidirect |
| 5. C53×#1345 | C2 | semidirect |
| 152. #11765 | C53 | direct (N × H) |
| 182. #1742 | C2×C53 | semidirect |
| 183. #1464 | C2×C53 | semidirect |
| 184. #1354 | C2×C53 | semidirect |
| 185. #1345 | C2×C53 | semidirect |
| 210. C53 | #11765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2610 | 2 |
| C53×#1742 | 2 |
| C53×#1464 | 2 |
| C53×#1354 | 2 |
| C53×#1345 | 2 |
| #11765 | 53 |