Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
124 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 61 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×#15690271 | C2 | semidirect |
| 2. C22×C191⋊C8 | C2 | semidirect |
| 3. C4⋊(C191⋊C8) | C2 | semidirect |
| 4. C22⋊(C191⋊C8) | C2 | semidirect |
| 5. C22⋊(C191⋊C8) | C2 | semidirect |
| 6. #20259233 | C2 | semidirect |
| 24. C191⋊C8 | D4 | semidirect |
| 42. C22×C191 | M16 | semidirect |
| 55. C191 | #435 | semidirect |
| 98. C22 | #15690271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690271 | 2 |
| C22×C191⋊C8 | 2 |
| C4⋊(C191⋊C8) | 2 |
| C22⋊(C191⋊C8) | 2 |
| #20259233 | 2 |
| C4×D4×C191 | 2 |
| #435 | 191 |