Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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. #41×#87604 | C2 | semidirect |
| 2. #20261732 | C2 | semidirect |
| 3. C2×#15690874 | C2 | semidirect |
| 4. #20261715 | C2 | semidirect |
| 5. #20261618 | C2 | semidirect |
| 6. #20261607 | C2 | semidirect |
| 24. #15690843 | C4 | semidirect |
| 25. #15690840 | C4 | semidirect |
| 27. #15690836 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C97 | C4 | semidirect |
| 59. C2×Dic194 | C2×C4 | semidirect |
| 73. #13095495 | C2×C4 | semidirect |
| 77. C2×D4×C97 | C2×C4 | semidirect |
| 80. M16×C97 | C2×C4 | semidirect |
| 151. C97 | #1906 | semidirect |
| 166. AGL(1,ℤ/8) | #87604 | semidirect |
| 199. C2×D4 | C2×#87604 | semidirect |
| 217. M16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#87604 | 2 |
| #20261732 | 2 |
| C2×#15690874 | 2 |
| #20261715 | 2 |
| #20261618 | 2 |
| #20261607 | 2 |
| #20261531 | 2 |
| #1906 | 97 |