Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20275888 | C2 | semidirect |
| 3. #20275691 | C2 | semidirect |
| 4. #20275383 | C2 | semidirect |
| 6. #20274863 | C2 | semidirect |
| 7. #20274817 | C2 | semidirect |
| 8. #20274519 | C2 | semidirect |
| 9. C53×#2102 | C2 | semidirect |
| 154. #2102 | D53 | semidirect |
| 188. C53 | #29232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276002 | 2 |
| #20275888 | 2 |
| #20275691 | 2 |
| #20275383 | 2 |
| #20275217 | 2 |
| #20274863 | 2 |
| #20274817 | 2 |
| #20274519 | 2 |
| C53×#2102 | 2 |
| #29232 | 53 |