Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20268514 | C2 | semidirect |
| 3. #20268138 | C2 | semidirect |
| 4. #20268118 | C2 | semidirect |
| 5. #20268076 | C2 | semidirect |
| 6. #20268023 | C2 | semidirect |
| 7. #20267991 | C2 | semidirect |
| 8. #20267952 | C2 | semidirect |
| 9. C8×D412 | C2 | semidirect |
| 10. #20267786 | C2 | semidirect |
| 11. C4×Q16×C103 | C2 | semidirect |
| 128. C103 | #3304 | semidirect |
| 137. C4×Q16 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268514 | 2 |
| #20268463 | 2 |
| #20268138 | 2 |
| #20268118 | 2 |
| #20268076 | 2 |
| #20268023 | 2 |
| #20267991 | 2 |
| #20267952 | 2 |
| C8×D412 | 2 |
| #20267786 | 2 |
| C4×Q16×C103 | 2 |
| #3304 | 103 |