Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20268463 | C2 | semidirect |
| 2. #20268168 | C2 | semidirect |
| 3. #20267991 | C2 | semidirect |
| 4. #20267987 | C2 | semidirect |
| 5. #20267534 | C2 | semidirect |
| 6. #20267520 | C2 | semidirect |
| 7. Q8⋊C8×C103 | C2 | semidirect |
| 56. Q8×C103 | D8 | semidirect |
| 108. C103 | #1621 | semidirect |
| 114. Q8⋊C8 | D103 | semidirect |
| 164. Q8 | D824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268463 | 2 |
| #20268168 | 2 |
| #20267991 | 2 |
| #20267987 | 2 |
| #20267534 | 2 |
| #20267520 | 2 |
| Q8⋊C8×C103 | 2 |
| #1621 | 103 |