Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 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×#15690879 | C2 | semidirect |
| 2. C2×#15690873 | C2 | semidirect |
| 4. C2×#15690864 | C2 | semidirect |
| 5. (C2×#87604)⋊Q8 | C2 | semidirect |
| 20. C2×#13095500 | C4 | semidirect |
| 21. C2×#13095499 | C4 | semidirect |
| 22. C2×#13095498 | C4 | semidirect |
| 26. C2×SD16×C97 | C4 | semidirect |
| 102. C8×C97 | C22⋊C4 | semidirect |
| 103. #11715895 | C22⋊C4 | semidirect |
| 133. C97 | #1973 | semidirect |
| 148. C2×SD16 | #87604 | semidirect |
| 236. 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×#15690873 | 2 |
| C2×#15690872 | 2 |
| C2×#15690864 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261687 | 2 |
| C2×SD16×D97 | 2 |
| #1973 | 97 |