Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
662 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3153 | C2 | semidirect |
| 2. C23×#3109 | C2 | semidirect |
| 3. C23×#2631 | C2 | semidirect |
| 4. C23×#1533 | C2 | semidirect |
| 5. C23×#1514 | C2 | semidirect |
| 6. C23×#1490 | C2 | semidirect |
| 7. C23×#1288 | C2 | semidirect |
| 47. C23×C4⋊Q8 | D4 | semidirect |
| 48. C23×#127 | D4 | semidirect |
| 78. C23×#97 | D4 | semidirect |
| 79. C4×C8×C23 | D4 | semidirect |
| 142. #10018 | C23 | direct (N × H) |
| 194. #3153 | C2×C23 | semidirect |
| 195. #3109 | C2×C23 | semidirect |
| 196. #2631 | C2×C23 | semidirect |
| 197. #1533 | C2×C23 | semidirect |
| 198. #1514 | C2×C23 | semidirect |
| 199. #1490 | C2×C23 | semidirect |
| 200. #1288 | C2×C23 | semidirect |
| 274. C4⋊Q8 | D4×C23 | semidirect |
| 275. #127 | D4×C23 | semidirect |
| 305. #97 | D4×C23 | semidirect |
| 306. C4×C8 | D4×C23 | semidirect |
| 311. C23 | #10018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3153 | 2 |
| C23×#3109 | 2 |
| C23×#2631 | 2 |
| C23×#1533 | 2 |
| C23×#1514 | 2 |
| C23×#1490 | 2 |
| C23×#1288 | 2 |
| #10018 | 23 |