Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276512 | C2 | semidirect |
| 3. #20273472 | C2 | semidirect |
| 4. #20272680 | C2 | semidirect |
| 5. #20272678 | C2 | semidirect |
| 6. #20272676 | C2 | semidirect |
| 7. C53×#1331 | C2 | semidirect |
| 74. D8×C53 | M16 | semidirect |
| 97. Dic212 | M16 | semidirect |
| 161. #1331 | D53 | semidirect |
| 186. C53 | #11660 | semidirect |
| 237. D8 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133236 | 2 |
| #20276512 | 2 |
| #20273472 | 2 |
| #20272680 | 2 |
| #20272678 | 2 |
| #20272676 | 2 |
| C53×#1331 | 2 |
| #11660 | 53 |