Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20260775 | C2 | semidirect |
| 4. #20260604 | C2 | semidirect |
| 5. #20260503 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 20. #15690737 | C4 | semidirect |
| 30. #13095495 | C2×C4 | semidirect |
| 43. C4×Dic97 | C2×C4 | semidirect |
| 62. Q8×C97 | C4⋊C4 | semidirect |
| 66. D4×C97 | C4⋊C4 | semidirect |
| 113. C97 | #1859 | semidirect |
| 175. Q8 | #13095490 | semidirect |
| 179. D4 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261218 | 2 |
| #20260775 | 2 |
| C2×#15690737 | 2 |
| #20260604 | 2 |
| #20260503 | 2 |
| #20260496 | 2 |
| #417×C97 | 2 |
| #1859 | 97 |