Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14541920 | C2 | semidirect |
| 2. #14538504 | C2 | semidirect |
| 3. #14538446 | C2 | semidirect |
| 4. C2×#11762620 | C2 | semidirect |
| 5. #14530513 | C2 | semidirect |
| 6. #14526883 | C2 | semidirect |
| 7. C17×#2117 | C2 | semidirect |
| 57. C2×Dic68 | D4 | semidirect |
| 67. C2×D136 | D4 | semidirect |
| 75. C2×C16×C17 | D4 | semidirect |
| 80. #10587490 | D4 | semidirect |
| 206. #2117 | D17 | semidirect |
| 305. C2×C16 | C22⋊D17 | semidirect |
| 314. C17 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541920 | 2 |
| #14538504 | 2 |
| #14538446 | 2 |
| C2×#11762620 | 2 |
| #14530513 | 2 |
| #14526883 | 2 |
| C17×#2117 | 2 |
| #13318 | 17 |