Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 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. C22×#13095495 | C2 | semidirect |
| 3. C2×#15690726 | C2 | semidirect |
| 4. #20260503 | C2 | semidirect |
| 5. #407×C97 | C2 | semidirect |
| 34. #13095495 | D4 | semidirect |
| 93. C22×C97 | #100 | semidirect |
| 114. C97 | #1900 | semidirect |
| 118. #407 | D97 | semidirect |
| 211. C22 | #15690726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095495 | 2 |
| C2×#15690784 | 2 |
| C2×#15690726 | 2 |
| #20260503 | 2 |
| #407×C97 | 2 |
| #1900 | 97 |