Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20285292 | C2 | semidirect |
| 2. #20276990 | C2 | semidirect |
| 3. #20276938 | C2 | semidirect |
| 4. #20276798 | C2 | semidirect |
| 5. D16×Dic53 | C2 | semidirect |
| 6. C4×C16×D53 | C2 | semidirect |
| 7. C53×#2246 | C2 | semidirect |
| 75. C16×C53 | #41 | semidirect |
| 95. C4×D53 | D16 | semidirect |
| 119. #2246 | D53 | semidirect |
| 145. C53 | #33733 | semidirect |
| 198. C16 | #11719947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285292 | 2 |
| #20276990 | 2 |
| #20276938 | 2 |
| #20276798 | 2 |
| D16×Dic53 | 2 |
| C4×C16×D53 | 2 |
| C53×#2246 | 2 |
| #33733 | 53 |