Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20274856 | C2 | semidirect |
| 3. #20273490 | C2 | semidirect |
| 4. #20273486 | C2 | semidirect |
| 7. C53×#1275 | C2 | semidirect |
| 135. #1275 | D53 | semidirect |
| 154. C53 | #10659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275513 | 2 |
| #20274856 | 2 |
| #20273490 | 2 |
| #20273486 | 2 |
| #20273141 | 2 |
| C53×#1275 | 2 |
| #10659 | 53 |