Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D17 | C2 | semidirect |
| 2. C2×D272 | C2 | semidirect |
| 3. C2×#10587497 | C2 | semidirect |
| 4. #11763046 | C2 | semidirect |
| 5. #11762609 | C2 | semidirect |
| 6. #11762588 | C2 | semidirect |
| 7. C17×#357 | C2 | semidirect |
| 14. C2×D136 | C22 | semidirect |
| 17. C2×C16×C17 | C22 | semidirect |
| 18. C17×#107 | C22 | semidirect |
| 20. C2×#63214 | C22 | semidirect |
| 33. D8×C17 | D4 | semidirect |
| 42. D136 | D4 | semidirect |
| 84. C2×D17 | D16 | semidirect |
| 94. #357 | D17 | semidirect |
| 115. C2×C16 | C2×D17 | semidirect |
| 116. #107 | C2×D17 | semidirect |
| 118. C17 | #2184 | semidirect |
| 134. D8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D17 | 2 |
| C2×D272 | 2 |
| C2×#10587497 | 2 |
| #11763046 | 2 |
| #11762609 | 2 |
| #11762588 | 2 |
| C17×#357 | 2 |
| #2184 | 17 |