Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 602 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 |
|---|---|---|
| 2. #20280073 | C2 | semidirect |
| 3. #20273275 | C2 | semidirect |
| 4. #20273144 | C2 | semidirect |
| 5. #20273107 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#3103 | C2 | semidirect |
| 110. C2×D212 | SD16 | semidirect |
| 226. #3103 | D53 | semidirect |
| 265. C53 | #9998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284175 | 2 |
| #20280073 | 2 |
| #20273275 | 2 |
| #20273144 | 2 |
| #20273107 | 2 |
| #20272574 | 2 |
| C53×#3103 | 2 |
| #9998 | 53 |