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 |
|---|---|---|
| 1. #20284747 | C2 | semidirect |
| 3. #20280069 | C2 | semidirect |
| 4. #20273276 | C2 | semidirect |
| 5. #20273145 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1478 | C2 | semidirect |
| 90. C2×D4×C53 | SD16 | semidirect |
| 231. #1478 | D53 | semidirect |
| 265. C53 | #9998 | semidirect |
| 335. C2×D4 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284747 | 2 |
| #20284179 | 2 |
| #20280069 | 2 |
| #20273276 | 2 |
| #20273145 | 2 |
| #20272574 | 2 |
| C53×#1478 | 2 |
| #9998 | 53 |