Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #20272779 | C2 | semidirect |
| 4. #20272778 | C2 | semidirect |
| 5. C53×#1367 | C2 | semidirect |
| 76. C8×C53 | M32 | semidirect |
| 82. #88322 | M32 | semidirect |
| 100. #1367 | D53 | semidirect |
| 116. C53 | #11996 | semidirect |
| 181. C8 | #13133156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276469 | 2 |
| C82×D53 | 2 |
| #20272779 | 2 |
| #20272778 | 2 |
| C53×#1367 | 2 |
| #11996 | 53 |