Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #381 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C22×D4×C53 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C53×#1300 | C2 | semidirect |
| 5. C53×#1288 | C2 | semidirect |
| 136. #8773 | C53 | direct (N × H) |
| 165. #1300 | C2×C53 | semidirect |
| 166. #1288 | C2×C53 | semidirect |
| 191. C53 | #8773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2353 | 2 |
| C4×#100×C53 | 2 |
| C53×#1466 | 2 |
| C53×#1300 | 2 |
| C53×#1288 | 2 |
| #8773 | 53 |