Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11763212 | C2 | semidirect |
| 3. #11763182 | C2 | semidirect |
| 4. #11763157 | C2 | semidirect |
| 5. #11763155 | C2 | semidirect |
| 6. C8×#3622 | C2 | semidirect |
| 7. C17×#492 | C2 | semidirect |
| 55. C8×C17 | D8 | semidirect |
| 57. #3622 | SD16 | semidirect |
| 74. #492 | D17 | semidirect |
| 96. C17 | #1706 | semidirect |
| 133. C8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763212 | 2 |
| #11763185 | 2 |
| #11763182 | 2 |
| #11763157 | 2 |
| #11763155 | 2 |
| C8×#3622 | 2 |
| C17×#492 | 2 |
| #1706 | 17 |