Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #20261648 | C2 | direct (N × H) |
| 12. C2×Dic388 | C4 | semidirect |
| 16. Q16×D97 | C4 | semidirect |
| 19. C2×Q16×C97 | C4 | semidirect |
| 33. Dic388 | C2×C4 | semidirect |
| 43. Q16×C97 | C2×C4 | semidirect |
| 80. C2×C97 | #358 | semidirect |
| 82. D97 | #358 | semidirect |
| 86. C97 | C2×#358 | semidirect |
| 98. C2×Q16 | #87604 | semidirect |
| 121. Q16 | C2×#87604 | semidirect |
| 169. C2 | #20261648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690883 | 2 |
| C2×#15690879 | 2 |
| #20261648 | 2 |
| C2×Q16×D97 | 2 |
| C2×#358 | 97 |