Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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×#15690879 | C2 | semidirect |
| 2. C2×#15690872 | C2 | semidirect |
| 3. C2×C8×#87604 | C2 | semidirect |
| 4. #20261687 | C2 | semidirect |
| 14. C2×D776 | C4 | semidirect |
| 15. C2×#13095496 | C4 | semidirect |
| 19. C2×D8×C97 | C4 | semidirect |
| 57. C2×#87604 | D8 | semidirect |
| 71. C8×C97 | C22⋊C4 | semidirect |
| 72. #11715895 | C22⋊C4 | semidirect |
| 99. C97 | #1970 | semidirect |
| 110. C2×D8 | #87604 | semidirect |
| 171. C8 | C22⋊#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| C2×#15690872 | 2 |
| C2×C8×#87604 | 2 |
| #20261687 | 2 |
| C2×D8×D97 | 2 |
| #1970 | 97 |