Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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×#15690878 | C2 | semidirect |
| 4. #20261609 | C2 | semidirect |
| 13. C2×#13095495 | C4 | semidirect |
| 14. C2×#13095494 | C4 | semidirect |
| 15. C2×#13095494 | C4 | semidirect |
| 20. C2×M16×C97 | C4 | semidirect |
| 83. C8×C97 | C22⋊C4 | semidirect |
| 85. #11715895 | C22⋊C4 | semidirect |
| 114. C97 | #1809 | semidirect |
| 126. C2×M16 | #87604 | semidirect |
| 199. 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×#15690878 | 2 |
| #20261677 | 2 |
| #20261609 | 2 |
| C2×M16×D97 | 2 |
| #1809 | 97 |