Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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. C23×#11764308 | C2 | semidirect |
| 2. C2×C22⋊#11764308 | C2 | semidirect |
| 3. C2×C22⋊#11764308 | C2 | semidirect |
| 4. (C2×#11764308)⋊C4 | C2 | semidirect |
| 14. C2×D1108 | C4 | semidirect |
| 15. C2×C22⋊D277 | C4 | semidirect |
| 16. C2×C22⋊D277 | C4 | semidirect |
| 20. C2×D4×C277 | C4 | semidirect |
| 27. C2×#11764308 | D4 | semidirect |
| 35. C22×D277 | C2×C4 | semidirect |
| 42. C2×Dic277 | C2×C4 | semidirect |
| 46. C23×C277 | C2×C4 | semidirect |
| 48. C2×C4×C277 | C2×C4 | semidirect |
| 52. C22×C277 | C22⋊C4 | semidirect |
| 63. C2×D277 | C22⋊C4 | semidirect |
| 81. C277 | #386 | semidirect |
| 95. C2×D4 | #11764308 | semidirect |
| 115. C23 | C2×#11764308 | semidirect |
| 130. C2×C4 | C2×#11764308 | semidirect |
| 148. C22 | C22⋊#11764308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11764308 | 2 |
| C2×C22⋊#11764308 | 2 |
| (C2×#11764308)⋊C4 | 2 |
| C2×D4×D277 | 2 |
| #386 | 277 |