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. #14538505 | C2 | semidirect |
| 3. #14538447 | C2 | semidirect |
| 4. C2×#11762618 | C2 | semidirect |
| 5. #14530511 | C2 | semidirect |
| 6. #14530411 | C2 | semidirect |
| 7. C17×#1383 | C2 | semidirect |
| 46. C2×Dic68 | D4 | semidirect |
| 57. C2×D136 | D4 | semidirect |
| 72. C2×C16×C17 | D4 | semidirect |
| 74. C17×#108 | D4 | semidirect |
| 207. #1383 | D17 | semidirect |
| 305. C2×C16 | D68 | semidirect |
| 307. #108 | D68 | 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 |
| #14538505 | 2 |
| #14538447 | 2 |
| C2×#11762618 | 2 |
| #14530511 | 2 |
| #14530411 | 2 |
| C17×#1383 | 2 |
| #13318 | 17 |