Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×Dic388 | C2 | semidirect |
| 3. #20260976 | C2 | direct (N × H) |
| 4. C2×#15690744 | C2 | semidirect |
| 5. C2×#15690735 | C2 | semidirect |
| 9. C2×Dic388 | C22 | semidirect |
| 15. #15690744 | C22 | semidirect |
| 16. #15690735 | C22 | semidirect |
| 47. C23×C97 | Q16 | semidirect |
| 73. C22×C97 | C2×Q16 | semidirect |
| 83. C2×C97 | #467 | semidirect |
| 88. C97 | C2×#467 | semidirect |
| 135. C23 | Dic388 | semidirect |
| 161. C22 | C2×Dic388 | semidirect |
| 171. C2 | #20260976 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic388 | 2 |
| C2×#15690789 | 2 |
| #20260976 | 2 |
| C2×#15690744 | 2 |
| C2×#15690735 | 2 |
| C23×C8×C97 | 2 |
| C2×#467 | 97 |