Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
552 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 213 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×#14555768 | C2 | semidirect |
| 3. #22581030 | C2 | direct (N × H) |
| 4. C2×(C2×D139)⋊C8 | C2 | semidirect |
| 5. C2×C4×C139⋊C8 | C2 | semidirect |
| 6. C2×C4⋊C8×C139 | C2 | semidirect |
| 10. C2×#14555768 | C22 | semidirect |
| 17. (C2×D139)⋊C8 | C22 | semidirect |
| 18. C4×C139⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C139 | C22 | semidirect |
| 32. C2×C139⋊C8 | D4 | semidirect |
| 55. C139⋊C8 | C2×D4 | semidirect |
| 58. C2×C4×C139 | M16 | semidirect |
| 76. C4×C139 | C2×M16 | semidirect |
| 80. C2×C139 | #436 | semidirect |
| 85. C139 | C2×#436 | semidirect |
| 90. C2×C4⋊C8 | D139 | semidirect |
| 105. C4⋊C8 | C2×D139 | semidirect |
| 142. C2×C4 | #14555768 | semidirect |
| 163. C4 | C2×#14555768 | semidirect |
| 167. C2 | #22581030 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555768 | 2 |
| C2×C4×D556 | 2 |
| #22581030 | 2 |
| C2×(C2×D139)⋊C8 | 2 |
| C2×C4×C139⋊C8 | 2 |
| C2×C4⋊C8×C139 | 2 |
| C2×#436 | 139 |