Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20268589 | C2 | semidirect |
| 2. C2×#15693046 | C2 | semidirect |
| 3. #20268360 | C2 | semidirect |
| 4. #20267809 | C2 | semidirect |
| 5. #20267795 | C2 | semidirect |
| 6. #20267561 | C2 | semidirect |
| 7. #410×C103 | C2 | semidirect |
| 56. #13110089 | D4 | semidirect |
| 58. C2×C103⋊C8 | D4 | semidirect |
| 64. C2×Q8×C103 | D4 | semidirect |
| 66. C2×D4×C103 | D4 | semidirect |
| 143. C103 | #2008 | semidirect |
| 149. #410 | D103 | semidirect |
| 184. C2×Q8 | D412 | semidirect |
| 195. C2×D4 | D412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268589 | 2 |
| C2×#15693046 | 2 |
| #20268360 | 2 |
| #20267809 | 2 |
| #20267795 | 2 |
| #20267561 | 2 |
| #410×C103 | 2 |
| #2008 | 103 |