Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20273279 | C2 | semidirect |
| 4. #20273144 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#3104 | C2 | semidirect |
| 100. C2×D212 | Q16 | semidirect |
| 208. #3104 | D53 | semidirect |
| 246. C53 | #10002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284508 | 2 |
| #20280073 | 2 |
| #20273279 | 2 |
| #20273144 | 2 |
| #20273107 | 2 |
| #20272574 | 2 |
| C53×#3104 | 2 |
| #10002 | 53 |