Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1262 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 207 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. #22571124 | C2 | semidirect |
| 2. #22565208 | C2 | semidirect |
| 3. #22559144 | C2 | semidirect |
| 4. #22558704 | C2 | semidirect |
| 5. #22558533 | C2 | semidirect |
| 6. C67×#3497 | C2 | semidirect |
| 101. C2×Q8×C67 | D8 | semidirect |
| 197. #3497 | D67 | semidirect |
| 203. C67 | #18401 | semidirect |
| 283. C2×Q8 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22565208 | 2 |
| #22559144 | 2 |
| #22558704 | 2 |
| #22558533 | 2 |
| C67×#3497 | 2 |
| #18401 | 67 |