Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1230 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 427 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 |
|---|---|---|
| 3. #22560363 | C2 | semidirect |
| 4. #22560362 | C2 | semidirect |
| 5. C67×#1843 | C2 | semidirect |
| 75. D67 | #1843 | direct (N × H) |
| 80. #1843 | D67 | direct (N × H) |
| 81. C67 | C2×#1843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C8×D67 | 2 |
| #376×D67 | 2 |
| #22560363 | 2 |
| #22560362 | 2 |
| C67×#1843 | 2 |
| C2×#1843 | 67 |