Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. C2×#15690808 | C2 | semidirect |
| 5. #20260745 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 7. C2×#101×C97 | C2 | semidirect |
| 126. C97 | #2005 | semidirect |
| 132. C2×#101 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| #20261309 | 2 |
| C2×#15690808 | 2 |
| C2×#15690736 | 2 |
| #20260745 | 2 |
| #20260496 | 2 |
| C2×#101×C97 | 2 |
| #2005 | 97 |