Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#3633 |
| commutator, socle | C2×C17 | C2×C4×C8 |
| Fitting | M16×C17 | C8 |
| prime radical | C22×D17 | C42 |
| cosocle | C4×#595 | C23 |
| hypercenter | M16 | #3633 |
| hypocenter | C17 | C8×M16 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11763893 | C2 | semidirect |
| 4. C8×#3633 | C2 | semidirect |
| 25. #63247 | C8 | semidirect |
| 30. #63243 | C8 | semidirect |
| 32. M16×C17 | C8 | semidirect |
| 33. #63223 | C8 | semidirect |
| 34. #63218 | C8 | semidirect |
| 45. #3633 | M16 | direct (N × H) |
| 52. #3624 | C2×C8 | semidirect |
| 53. C8×C17 | C2×C8 | semidirect |
| 54. #3622 | C2×C8 | semidirect |
| 91. C17 | C8×M16 | semidirect |
| 99. M16 | #3633 | direct (N × H) |
| 128. C8 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| C2×C4×#3633 | 2 |
| #11763893 | 2 |
| C8×#3633 | 2 |
| M16×#595 | 2 |
| C8×M16 | 17 |