Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
924 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#16810996 | C2 | semidirect |
| 2. C2×#16810682 | C2 | semidirect |
| 3. #20280484 | C2 | semidirect |
| 5. #20276034 | C2 | semidirect |
| 6. #20275721 | C2 | semidirect |
| 7. #20275538 | C2 | semidirect |
| 8. #20275534 | C2 | semidirect |
| 9. C53×#1835 | C2 | semidirect |
| 68. C4×C8×C53 | D4 | semidirect |
| 184. #1835 | D53 | semidirect |
| 214. C53 | #29811 | semidirect |
| 249. C4×C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810996 | 2 |
| C2×#16810682 | 2 |
| #20280484 | 2 |
| #20280468 | 2 |
| #20276034 | 2 |
| #20275721 | 2 |
| #20275538 | 2 |
| #20275534 | 2 |
| C53×#1835 | 2 |
| #29811 | 53 |