Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#15690878 | C2 | semidirect |
| 2. C2×#15690872 | C2 | semidirect |
| 3. C2×#15690864 | C2 | semidirect |
| 4. #20261687 | C2 | semidirect |
| 14. C2×D776 | C4 | semidirect |
| 15. C2×#13095496 | C4 | semidirect |
| 19. C2×D8×C97 | C4 | semidirect |
| 70. C8×C97 | C22⋊C4 | semidirect |
| 71. #11715895 | C22⋊C4 | semidirect |
| 96. C97 | #1972 | semidirect |
| 107. C2×D8 | #87604 | semidirect |
| 167. C8 | C22⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690878 | 2 |
| C2×#15690872 | 2 |
| C2×#15690864 | 2 |
| #20261687 | 2 |
| C2×D8×D97 | 2 |
| #1972 | 97 |