Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #14545926 | C2 | semidirect |
| 3. #14545909 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545789 | C2 | semidirect |
| 67. C17×#104 | C8 | semidirect |
| 68. #10587508 | C8 | semidirect |
| 69. #10587496 | C8 | semidirect |
| 70. #10587476 | C8 | semidirect |
| 118. M16×C17 | C2×C8 | semidirect |
| 119. C42×C17 | C2×C8 | semidirect |
| 121. C4×Dic17 | C2×C8 | semidirect |
| 122. #63223 | C2×C8 | semidirect |
| 269. #104 | #3633 | semidirect |
| 278. C17 | #8840 | semidirect |
| 300. M16 | C2×#3633 | semidirect |
| 332. C42 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546028 | 2 |
| #14545926 | 2 |
| #14545909 | 2 |
| #14545903 | 2 |
| #14545796 | 2 |
| #14545789 | 2 |
| #104×#595 | 2 |
| #8840 | 17 |