Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690734 | C2 | semidirect |
| 2. C2×#15690731 | C2 | semidirect |
| 3. C2×C22⋊#11715895 | C2 | semidirect |
| 4. #20260595 | C2 | semidirect |
| 16. C2×#41×C97 | C4 | semidirect |
| 66. Q8×C97 | C22⋊C4 | semidirect |
| 70. D4×C97 | C22⋊C4 | semidirect |
| 116. C97 | #1788 | semidirect |
| 125. C2×#41 | Dic97 | semidirect |
| 182. Q8 | C22⋊Dic97 | semidirect |
| 186. D4 | C22⋊Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690734 | 2 |
| C2×#15690731 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260595 | 2 |
| C22×#41×C97 | 2 |
| #1788 | 97 |