Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #1361 |
| commutator | C2×C16 | C2×C4×C53 |
| Frattini, cosocle | C4×C16 | C22×C53 |
| prime radical | C53×#2246 | C2 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C4×C8×C53 ◁ C4×C16×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1422 | C2 | semidirect |
| 3. C53×#1373 | C2 | semidirect |
| 44. #7448 | C53 | direct (N × H) |
| 52. #1422 | C2×C53 | semidirect |
| 53. #1373 | C2×C53 | semidirect |
| 63. C53 | #7448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2246 | 2 |
| C53×#1422 | 2 |
| C53×#1373 | 2 |
| #7448 | 53 |