Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20260778 | C2 | semidirect |
| 4. #20260604 | C2 | semidirect |
| 5. #20260504 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 15. #15690737 | C4 | semidirect |
| 31. #13095495 | C2×C4 | semidirect |
| 38. C4×Dic97 | C2×C4 | semidirect |
| 62. Q8×C97 | C4⋊C4 | semidirect |
| 66. D4×C97 | C4⋊C4 | semidirect |
| 113. C97 | #1859 | semidirect |
| 175. Q8 | #13095490 | semidirect |
| 179. D4 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260778 | 2 |
| C2×#15690737 | 2 |
| #20260736 | 2 |
| #20260604 | 2 |
| #20260504 | 2 |
| #20260494 | 2 |
| #520×C97 | 2 |
| #1859 | 97 |