Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #20272680 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 6. #20272678 | C2 | semidirect |
| 7. C53×#1332 | C2 | semidirect |
| 73. Q16×C53 | M16 | semidirect |
| 97. Dic212 | M16 | semidirect |
| 157. #1332 | D53 | semidirect |
| 181. C53 | #11658 | semidirect |
| 231. Q16 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D53 | 2 |
| #20276512 | 2 |
| #20273472 | 2 |
| #20272680 | 2 |
| #20272679 | 2 |
| #20272678 | 2 |
| C53×#1332 | 2 |
| #11658 | 53 |