Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 199 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. #20276997 | C2 | semidirect |
| 3. #20276996 | C2 | semidirect |
| 4. #20276995 | C2 | semidirect |
| 7. C53×#2254 | C2 | semidirect |
| 35. C16×D53 | Q8 | semidirect |
| 70. C16×C53 | C2×Q8 | semidirect |
| 71. #11719908 | C2×Q8 | semidirect |
| 105. #2254 | D53 | direct (N × H) |
| 110. D53 | #2254 | direct (N × H) |
| 127. C53 | C2×#2254 | semidirect |
| 175. C16 | Q8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D53 | 2 |
| #20276997 | 2 |
| #20276996 | 2 |
| #20276995 | 2 |
| #367×D53 | 2 |
| C4×C16×D53 | 2 |
| C53×#2254 | 2 |
| C2×#2254 | 53 |