Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1092 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2856 | C2 | semidirect |
| 2. C13×#2071 | C2 | semidirect |
| 3. C13×#2011 | C2 | semidirect |
| 4. C13×#1999 | C2 | semidirect |
| 5. C13×#1817 | C2 | semidirect |
| 45. #32758 | C13 | direct (N × H) |
| 68. C22×C4×C13 | D8 | semidirect |
| 84. #2856 | C2×C13 | semidirect |
| 85. #2071 | C2×C13 | semidirect |
| 86. #2011 | C2×C13 | semidirect |
| 87. #1999 | C2×C13 | semidirect |
| 88. #1817 | C2×C13 | semidirect |
| 214. C22×C4 | C13×D8 | semidirect |
| 230. C13 | #32758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2856 | 2 |
| C13×#2071 | 2 |
| C13×#2011 | 2 |
| C13×#1999 | 2 |
| C13×#1817 | 2 |
| #32758 | 13 |