Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
630 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#2537 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1844 | C2 | semidirect |
| 3. C53×#1802 | C2 | semidirect |
| 4. C2×C53×D4⋊C8 | C2 | semidirect |
| 5. C53×#1296 | C2 | semidirect |
| 42. C4×C8×C53 | D4 | semidirect |
| 120. #10432 | C53 | direct (N × H) |
| 143. #1844 | C2×C53 | semidirect |
| 144. #1802 | C2×C53 | semidirect |
| 145. C2×D4⋊C8 | C2×C53 | semidirect |
| 146. #1296 | C2×C53 | semidirect |
| 165. C53 | #10432 | direct (N × H) |
| 190. C4×C8 | D4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2537 | 2 |
| C53×#1844 | 2 |
| C53×#1802 | 2 |
| C2×C53×D4⋊C8 | 2 |
| C53×#1296 | 2 |
| #10432 | 53 |