Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 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. #20261363 | C2 | semidirect |
| 4. #20260503 | C2 | semidirect |
| 5. #20260496 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 49. C2×D4×C97 | Q8 | semidirect |
| 113. C97 | #2027 | semidirect |
| 145. C2×D4 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20260740 | 2 |
| #20260638 | 2 |
| #20260503 | 2 |
| #20260496 | 2 |
| #20260494 | 2 |
| #418×C97 | 2 |
| #2027 | 97 |