Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 118 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 | #1333 |
| commutator | C16 | C2×C8×C53 |
| Frattini, cosocle | #346 | C22×C53 |
| prime radical | C53×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C4×C8×C53 ◁ C53×#346 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1398 | C2 | semidirect |
| 3. C53×#1368 | C2 | semidirect |
| 13. Q32×C53 | C8 | semidirect |
| 15. D16×C53 | C8 | semidirect |
| 48. #7389 | C53 | direct (N × H) |
| 56. #1398 | C2×C53 | semidirect |
| 57. #1368 | C2×C53 | semidirect |
| 68. C53 | #7389 | direct (N × H) |
| 71. Q32 | C8×C53 | semidirect |
| 73. D16 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2179 | 2 |
| C53×#1398 | 2 |
| C53×#1368 | 2 |
| #7389 | 53 |